Youtube comments of (@Gametheory101).

  1. Small correction at 19:22: The fall of the U.S.-backed government in Afghanistan occurred in 2021, not 2022. And 26:16 is “Siberia”, not “Serbia”. Though I do wonder if a hypothetical ice fisher in Serbia is also aware of Russian corruption.
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  2. Correction at 5:00 It was Columbia that broke apart, not Discovery.
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  3. Don't skip the outro at 17:01! I have been waiting six years to find the right time to tell that story, and it is basically it's own mini video.
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  4. 4:30 Should be Fahrenheit, or 93 degrees Celsius. Obviously, 200C can boil things.
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  5. I produced this video just a few hours after the attack. The situation and the facts on the ground are rapidly changing, so keep that in mind as you are watching it. As with all of my videos, the main thing I want you to take away is the overall strategic issues at play, which extend beyond a single attack.
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  6. For the segment at 9:35: my goal for this is not to make a blanket claim that nuclear weapons have never affected any calculations at the periphery, just that the historical record is not as good as it may seem. I struggled writing that section, trying to weigh completeness versus not going down a history rabbit hole and sidetracking the main point of the video. Hope that is clear. This is not how I would go about addressing the question if this were a true research setting!
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  7. I wanted to get this out ASAP after the election, so there are a few things that I did not go into: how the Biden administration could counteract the problem over the next three months, what Ukraine could be doing as well, and whether either Kyiv or Moscow might try to do to through a wrench into a potential peace plan. We'll have to save all of those for another day!
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  8. Anything interesting happening in South Korea today?
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  9. 1:24:00 I feel like the woman's shirt in the bottom left corner is a microcosm of everything in this video.
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  10. Is a dam gamble just a damble?
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  11. I know a lot of you were re-watching the video on the dam from three months ago. A lot of this will sound familiar, but there are important updates regarding the water level prior to the dam's failure and how the nuclear power plant is doing. Apologies for the choppiness on some of the animations here---I didn't have time to get everything as clean as I would want. My goal was to get this out ASAP given how important of a moment this is in the war.
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  12. The joys of commentary as a situation is unfolding! Here's are my updated thoughts given the announcement that Wagner is turning around: 0:00 This is still a good summary up until this morning. 1:44 We will need to keep an eye on whether this affects Rostov-on-Don's ability to resupply. I noted in the video that Wagner was not actually stopping anything, so not much has changed. It's still a big concern for Russia if anything does happen. 3:24 This is how coups work broadly, so it's still a useful watch. Unclear whether the reason Prigozhin backed down was because he was not getting enough momentum fast enough. 6:56 The rally this will give the West is probably the biggest takeaway from the whole affair, assuming nothing else weird happens 8:29 The affair did not go on long enough to give Putin political cover to vacate, but it is something to keep in mind if the internal conflict recurs.
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  13. This comment is sus.
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  14. Now this is the content I was hoping to read.
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  15. Correction: at 9:44 it should be eastward (as the map illustrates), not westward.
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  16. What would you like to know about Trump/Iran/Israel? I want ideas for the next video!
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  17. 17:02 Over-analysis of politicians on chairs
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  18. Bad news everyone: I just exhausted all of my photos of Putin with binoculars. Also, 6:44 should be "positive and neutral are the same".
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  19. 1:06 October 7, not October 6. Sorry guys, it was a sleepless night putting this together. Also, standard caveat that the situation is fluid, and so everything I said here was according to the world's understanding at the time of writing.
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  20. It’s lack of sleep! Zero interns or any one else for that matter.
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  21. Sadly, this actually happened two nights ago.
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  22. Short note: There has been at least one more strike and perhaps two since I produced this video. Longer explanation: I produced this weekends ago, with plans to publish it last week. Then the Iran/Israel exchange happened, which delayed publication. Sorry!
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  23. Another fun fact about Uriah: David recalled Uriah from the front lines and desperately tried to get him to spend the night with Bathsheba to cover for the pregnancy. He steadfastly refused out of solidarity for the rest of the unit. Ironically, that caused his death.
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  24. 1:10 LINES ON MARS
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  25. Because I didn’t want this to turn into a 30+ minute monster (and also I am facing a deadline), there is a lot of nuance missing from this video. Here are some extra notes: 6:24 There is a lot of debate whether using ATACMS would be a wise military idea. My description here is not an assessment of that, just that there is going to be renewed attention to the bridge. 9:02 By more sophisticated measures of ideology, Joe Manchin (D-West Virginia) is the pivotal voter in the Senate. The filibuster-proof pivot is John Hoeven (R-North Dakota). 10:10 I’m not making that up. 13:40 That is Paul Ryan’s official Speaker of the House portrait, but you would be forgiven if you thought it was AI drawn. 14:01 That is supposed to be 108, not 109. 20:44 Ganon has been vanquished. 21:21 Because the president is the commander-in-chief, trying to work around a veto would be difficult in practice. Also, Biden still needs to sign the bill, but that is the easiest part.
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  26. Note: In the couple of days since I recorded this, Russia has made a bit further progress along the salient and is now threatening the next town in line. It is not a huge development but still something to keep an eye on.
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  27. Russia captured Avdiivka while I was producing this video, which is why it is discussed here but not the focus. Later this week, I will give a broader update on the war in light of Ukraine's retreat.
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  28. Grab Atlas VPN with 83% off + 3 months EXTRA using my link: get.atlasvpn.com/linesonmaps
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  29. The turn of the calendar year is the bane of my existence. Also, RIP me at 9:41.
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  30. How did I not notice this?!
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  31. Did you enjoy this video? Check out my new book based on it "What Caused the Russia-Ukraine War? (And How Will It End?)". It's a significant expansion on these ideas---the script for this video is about 6,000 words, whereas the book is 42,000. The digital version is out now available at https://amzn.to/3HY5aqW. You can also read it for free by signing up for a Kindle Unlimited trial at https://amzn.to/3QMsBr8. (These are affiliate links, meaning I earn a commission when you make a transaction through them. Even if you read it for free, you are still supporting the channel.) Physical edition coming soon!
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  32. Oh snap
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  33. 11:20 The camera man of first nuclear test ever HAD ONE JOB.
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  34. 13:37 Outtake
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  35. That’s grizzly
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  36. 7:54 Should be January 2022 border.
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  37. At this rate, the next video is going to be titled “Revenge of the Ayatollah”…
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  38. 1:21 February 2022, not February 2023. I knew the changing of the calendar was going to be the death of me, and I am sure it is only going to get worse now that we are in 2024. I also don't like how the average video has increased by ten seconds now that I have to specify which year everything is.
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  39. 8:23 Putin: I hate NATO. Zelensky: Why are we still talking about this? Merkel: Hey, Macron, check out this funny joke!
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  40. Yes, it is the "Vela Hotel incident"
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  41. It only took five minutes for the last one to be outdated 😅
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  42. 11:10 Update: Yesterday (after recording), it looks like Russia might have extended out to the rest of the housing that the line was previously going through. Just another thing to keep an eye on for the next few weeks. Actually, quite coincidentally, the front line now looks like what I hypothetically drew at 14:44.
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  43. Small corrections: 0:06 should be "half of a year" not "year and a half" 2:03 the bottom right photo is Storozheve, not Makarivka
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  44. September Update: Russia captured about 468 square kilometers of Ukraine and regained about 126 square kilometers in Kursk. This was Russia's biggest gain since March 2022. There are two main problems with this estimate now. First, the pace is increasing, so averaging out what has happened over almost a year is misleading. This biases toward a higher total. Second, Russia's observed equipment losses have massively spiked in the most recent couple of months. These are correlated with casualties. However, I am still using the 5000 losses/month from Putin's earlier comments. This biases toward a lower total. August 2024 Update: The Kursk offensive is causing a bit of a headache here. Russia gained 351 square kilometers of Ukraine, but Ukraine gained 770 square kilometers of Russia. If you are only looking at the first half, then the offensive's pace is 21.8 million. If you include both, then the Kursk losses undo all of Russia's gains back until May, and the number is 68.7 million. July 2024 Update: Russia had the second best month of its offensive, taking 0.03% of Ukrainian territory. This was much more than in June but still less than May. Still, the improved average lowered the number of remaining fatalities at the offensive's pace to 28 million and change.
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  45.  @weakspirit_  Right, it was sarcastic. The next sentence immediately pivots to "Lithuania was like lol no."
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  46. All the Star Wars easter eggs: 0:00 “Hello there” 5:48 “pathways to locations some consider to be unnatural” 14:19 “I am the Senate.” 20:18 “Who’s the more foolish?” 23:42 “This deal is getting worse all the time.” 24:12 Revenge of the Lines 29:04 “I have a bad feeling about this.” 35:40 “A surprise attack to be sure…” 36:14 May the Fourth 37:04 Mark Hamill cameo 41:48 Legal? 42:10 “It’s a trap!” 51:48 Execute Order 66 53:20 It’s over. Iran has the high ground. 54:05 I am your father. 55:37 “Somehow the Iranian mines returned.” 58:05 Reasons to hate sand 1:14:40 “Spinning is a good trick.” 1:17:28 “There’s always a bigger bomb.” 1:24:00 “The ability to draw lines does not make a theory intelligent.” 1:24:40 It’s treason then. 1:31:15 The tank is nicknamed Baby Yoda 1:32:12 “Now this is podcasting!”
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  47. DUDE
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  48. Thanks to Ground News for sponsoring this video! Sign up, get diverse headlines, and check your own media bias by signing up here: https://ground.news/linesonmaps
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  49. What episode was that from???
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  50. Bakhmut, halting Ukraine’s 2023 offensive, creating political lockdown in the West, increased air strikes in Western Ukraine, and Avdiivka. Obviously, this is not the end of the game for Ukraine, and other recent videos have covered some of the bright spots that Ukraine had had in recent months—in particular, on the Black Sea and the drone strikes on Russian infrastructure. The main point is that Russia has the initiative and quashed Ukraine’s most recent attempt to take it and make progress.
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  51. 3:44 What's amazing here is that I did not sync the "cannon fodder" line with the visual! In fact, I wasn't even aware there were cannons in the B-roll until I was in the middle of narrating the section.
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  52. Generally, longer is better for the algorithm. But there aren’t too many topics that can go 90 minutes without being boring, and boring is bad for the algorithm.
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  53. It helps that I almost exclusively do videos on topics connected to my research interests, so it double counts to some degree. For example, an academic version of the “Why Russia Miscalculated video got accepted at a peer-reviewed journal earlier this week.
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  54. All of the Zelda references: 6:12 "given the Link to the Past war of 2008" 6:49 "Let's turn back our Phantom Hourglasses" 8:03 "Its Spirit Tracks with a bygone era" 8:23 "The Oracle of Ages determined" 11:26 I intentionally mispronounced "cannon" as "Ganon" 13:19 "With the obvious Links Awakening an identical anger" 15:32 "The military acts as a Link between Worlds" 15:59 "they will soon find out that it is dangerous to go alone" 16:58 #wheresputin captures the Triforce. 18:00 "in this Age of Calamity" 22:26 Legend of Zelensky title card 22:31 "Hey, listen!" 23:28 "if you have the power, wisdom, and courage" 22:56 "the game where I Try Forcing the Russian leader"
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  55. Sorry I just need to go out and get a gallon of milk. I will be right back!
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  56. Yes, but it was 100 words longer, which meant that I saved about 14 seconds by talking faster. 😅
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  57. I realized after recording this that I made #whereseveryone way, way too hard. All of them (Prigozhin, Surovikin, Gerasimov) are in the image starting at 7:40. You may have to do some maneuvering around Zelensky to find them.
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  58. Can’t remember that episode, time to add it to the queue!
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  59. Yeah that should have been a lot more precise.
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  60. 6:56 Secretary of Defense Lloyd Austin. The joys of turning something around in six hours or less...
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  61. I see what you did there.
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  62. Certified first comment is a real comment!
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  63. Anything for a national treasure like Bob Saget.
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  64. I see you are one of the enlightened folks who know to skip straight to the outros. :)
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  65. Correction: The Molotov–Ribbentrop Pact was signed in August 1939, and operation Operation Barbarossa began in June 1941. That is the length of I should have cited for when it was broken, though there were some other things in between that made things dirty.
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  66. Beep boop
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  67. Next one is about the financial crisis that Russia has been quietly going through the last few months
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  68. Kaan Bursa I sincerely hope that was 90 or 99 out of 100 and not 9!
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  69. TIL. That may be outro worthy!
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  70. 15:46 The phone call in question was on December 2, 2016, not the date shown. Trump had won the 2016 election but was not yet president at the time that it occurred.
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  71. I’m so guilty
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  72. For everyone asking, here's the secondary channel: https://www.youtube.com/@LinesonMapsExtra
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  73. It was something like: Initial Writing: 2 hours Animating: 5 hours Voice Over: 1.5 hours Editing and YouTube: 1.5 hours I tend to add to the script as I animate and do voice over, though. This started at 900 words when I began animating and ended at about 1650.
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  74. 23 Easter eggs by my count…
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  75. That’s the best explanation I have seen for it, thank you!
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  76. This is a worthy first comment.
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  77. Thanks. Once I had a string of P-words next to each other, I spent way too much time revising the sentence so the whole thing would alliterate.
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  79. Yeah, it's a crazy coincidence. Wish I could have included it, but I filmed this one two days ago.
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  80. This video is dedicated to Katy Perry.
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  81. I know "Why Putin Didn't 'Cause' the War (But He Is Responsible for It)" won this week's vote, but then the Kaliningrad thing happened, so we're going with this for the week. I've scripted the Putin/cause video, though, so that's definitely happening soon. Also, with any luck, the digital version of my Ukraine book will be released next week!
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  82. I see that your parents also have very good taste.
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  83. Huge missed opportunity for for me there.
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  84. Busy, but good. Thanks for asking!
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  85. Oops, yes!
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  86. Go to https://ground.news/LinesOnMaps to stay fully informed on what's happening around the world. Subscribe through my link for 50% the Vantage plan for unlimited access, this month only.
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  87. Go to https://ground.news/LinesOnMaps to stay fully informed on what's happening around the world. Subscribe through my link for 50% the Vantage plan for unlimited access, this month only.
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  88. Hey man I’m in a hurry here!
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  89.  @ArawnOfAnnwn  Incorrectly believed I had, thanks!
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  90. I'm gonna go back to working on super-long form soon, so that might help!
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  91. Political economy!
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  92. Thank you so much! Very generous.
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  93. I was on an all-time best pace. Gold split after gold split after gold split. Then I had to re-render the video three times because of stupid editing mistakes.
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  94. Sign up for a 14-day free trial and enjoy all the amazing features MyHeritage has to offer https://bit.ly/WilliamSpaniel
    77
  95. Also: “anyway,” “however,” and “now.”
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  96. #facts
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  97. The original report from the NYTimes did not indicate this. Axios more recently reported the restriction. All of that is up in the air, of course.
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  98. Go to https://ground.news/linesonmaps to stay fully informed on what's happening around the world. Subscribe before month's end and you'll receive 40% off unlimited access!
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  99. There is self-interest in cooperating in the stag hunt. There is no self-interest in cooperating in a prisoner's dilemma.
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  100. Correction at 7:15: That's the price per 100 bushels, not the price per bushel. Because this is just a matter of scale, the general point stands: prices were up by a lot. (*Were* is the operative word here, because they have fallen back in place in the last few months.)
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  101. That would make sense!
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  102. Thanks for the input. The reporting and info from the front lines suggests that this is not the case, though the video does not cover the nuance, and I appreciate that we have fog of war so that reporting could be wrong and you could be right. The Ukrainian Zaporizhzhia government indicates that the main intent of lifting the sluices is to flood the other side. It is true that the water level release has been somewhat gradual (and, like you said, limits the level of flooding), but it seems that there is some effect. It is also reasonable to think that Russia would do this intentionally because they want some flooding but not a catastrophic amount. Regarding whether this is the product of an accident, NPR reports that the lifting of the gates was intentional. It is plausible that they got stuck, but it would then raise the question of why they lifted the sluices in the first place. But thanks again for your comment! It is great to hear another perspective with such detail.
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  103. I recorded this yesterday afternoon and this morning. The lack of an actual announcement is discussed around 3:00.
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  104. I try!
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  105. It’s at record lows. Water levels didn’t drop below 15.5 meters before the war. I should have mentioned this in the video. Whoopsie?
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  106. To be clear, "brothers" is sarcastic. I am well-aware of the Russia-Lithuania history. Anyway, if you enjoyed this video, check out my new book "What Caused the Russia-Ukraine War? (And How Will It End?)". It brings together the ideas from my recent video series into a coherent narrative. The digital version is out now available at https://amzn.to/3HY5aqW. You can also read it for free by signing up for a Kindle Unlimited trial at https://amzn.to/3QMsBr8. (These are affiliate links, meaning I earn a commission when you make a transaction through them. Even if you read it for free, you are still supporting the channel.) Physical edition coming soon!
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  107. Yay, I won!
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  108. My editor is me. :)
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  109. That may very well be the case. Something like that has been a recurring theme in my previous videos, but I definitely should have mentioned it again here.
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  110. When I woke up and saw the news, I was like "NOOOO I'M NOT GOING TO HAVE FUN TODAY"
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  111. Winner!
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  112. I missed an opportunity for a joke about lines in front of banks, oops.
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  113. Well, at least we have YouTube.
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  114. A certified first comment is on the horizon!
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  115. That would have been an awesome pun to include!
    56
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  117. Back by popular demand: LINES. ON. MAPS.
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  118. Holy moly
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  119. Certified first comment. We now know that < 19 seconds is what it takes!
    52
  120. Thanks---I was wondering why the red emblems looked Soviet-esque.
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  121. Go to https://ground.news/Will to stay fully informed on what's happening around the world. Subscribe through my link for 50% the Vantage plan for unlimited access, this month only.
    51
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    50
  123. Every time I start writing one of these, I feel like there are 80 different tangents I need to avoid going down otherwise the video will never be finished.
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  124. Next video is about the Battle of Ba Sing Se. It will be very short, of course, because there is no war in Ba Sing Se.
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  125. Sorry, friend.
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  126. Go to https://ground.news/LinesOnMaps to stay fully informed on what's happening around the world. Subscribe through my link for 50% the Vantage plan for unlimited access, this month only.
    49
  127. "All models are wrong"??? Only Sith deals in absolutes.
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  128. The players move simultaneously. Player 2 has no choice in the matter because she has no ability to control player 1's move, and player 1 has no reason to play up when he could play middle instead.
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  129. Better than Maester Aemon, who can't see anything at all.
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  130. I always knew the turn of calendar from 2022 to to 2023 was going to be the death of me, and it is only getting worse.
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  131. Go to https://ground.news/linesonmaps to stay fully informed on what's happening around the world. Subscribe before month's end and you'll receive 40% off unlimited access!
    45
  132. I didn't miss it! It is directly written into the subtitles!
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  133. True!
    45
  134. It's a jungle out there.
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  135. The slight fuel price increase will make living on the West Coast less attractive, and as a result he is more likely to finish his career back in Cleveland. True story.
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  136. Oh my bad
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  137. Yep, you are correct!
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  138. Right. But I was producing this over the last couple of weeks waiting for it to happen!
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  139. It varies by region. So that could still be true elsewhere.
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  140. I feel safe in saying that this is the first time that sentence has ever been written in the history of mankind.
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  141. Did you ever hear the tragedy of Darth Linezenmaps the Wise?
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  142. Thank you so much! That’s incredibly generous.
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  143. In season 41 of DS9, the "O'Brien goes through hell episode" is set in Russia!
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  144. The plan was that the next video would be about nukes, so let's hope it doesn't get too serious.
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  145. By clicking my link http://piavpn.com/linesonmaps you'll get an 83% discount on Private Internet Access! That's just $2.03 a month, and you'll also get 4 extra months completely for free!
    37
  146. Haters gonna hate.
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  148. "High" quality, you say?
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  149. I would, but that was in last place last time I ran a poll on potential topics.
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  150. Most of it is time and effort. A lot of mathematical thinking is trained, not innate. I barely passed my math classes in high school before taking this up as a career.
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  151. Certified first!
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  152. Then you have "stag hunt" preferences, which are covered a couple of videos from now. Remember: payoffs represent a player's preference--they do not mean a player MUST have those preferences. If you change the inputs of the game, you shouldn't be surprised if the outputs change as well. So if you have more cooperative preferences, it is possible to achieve cooperation.
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  153. Only twice today!
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  154. I will try harder!
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  155. I am not a lawyer, but at minimum NATO defines the area it covers as North America and Europe. So this might apply to an attack on the German embassy in Mexico, but it would not on the US embassy in Kenya. The latter seems to be what happened in practice given the 1998 African embassy bombings not triggering Article 5.
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  156. If both players stop, it's going to take them some time to figure out who is going to go first, which is bad for both of them. If I stop and you just go, then I know I can go immediately after you pass.
    33
  157. Yikes
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  158. I actually recorded this a month ago. The (more pressing) news elsewhere has been moving fast enough that I kept pushing the release date back.
    32
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  160. Do it!
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  161. Amazon recently started allowing INR purchases on the .com website. You might want to look into that.
    30
  162. I prefer "line-adult" 😢
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  163. “the jerk of international relations”
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  164. Go to https://ground.news/Will to stay fully informed on what's happening around the world. Subscribe through my link for 50% the Vantage plan for unlimited access, this month only.
    29
  165. Well, if you go deeper into this course, you will discover that there is also a mixed strategy Nash equilibrium. In it, each side sometimes yields and sometimes does not. The observable implications are pretty chaotic, just like what you described!
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  166. Third, but thank you!
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  167. 13:39 Not sure if Gaddafi is at the United Nations or World Series of Poker...
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  168. Everyone thought that the over-the-top raid had been optimized, and that no time saves were left. Then this happened.
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  169. Well then. I guess I need to take this one down and post an updated video.
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  170. I do not. All of these videos are 100% me.
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  171. It was a surprise to be sure, but hopefully a welcome one
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  172. You will be happy to know that I saluted General Feel as I was narrating that line.
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  173. I have a PhD in political science and I work full time as a professor.
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  174. Nice
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  175. Check the payoff matrix again. There are no strictly dominated strategies here. Recall that a strictly dominated strategy must always be WORSE than another strategy. If it is sometimes equally as good, then it is not strictly dominated. We cover this type of "weak dominance" later.
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  176. Was waiting for someone to pick up on this...
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  177. Snake?
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  178. Oh thank you!
    27
  179. Get up to 3 months of ProtonVPN for free ---> http://protonvpn.com/williamspaniel
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  180. Joey Burbs I'd rather be the shadowy backroom figure. :)
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  181. Your type might affect my payoffs. For example, suppose everyone knows I am a benevolent YouTube creator. But I don't know whether you are a troll or an interested learner. My payoff for responding to your comments definitely depends on your type.
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  182. Very true. I had “flu/COVID” in my notes for this video but ultimately cut it. I probably should have squeezed it in as just an add-on point for issues with staying warm.
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  183. After a brief break, we're back to LINES ON MAPS starting at 3:32!
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  184. +shafique dassu On a basic level, P1's mixed strategy should be called a P1's because P1 is the guy actually playing it, even if he is basing his mixture on P2's payoffs. For why we calculate P1's mixture using P2's payoffs, recall that Nash equilibrium requires that no player have a profitable deviation. Now suppose we suspect that a game has an equilibrium in mixed strategies. If I am randomizing between up and down, what does the requirement not having a profitable deviation say about my expected utilities for up and down? Well, they need to be equal. If they weren't, one would be greater than the other. I could therefore profitably deviate by playing the strategy that generates the greater expected utility. The only thing that can change the relative attractiveness of my two strategies is how often my opponent is playing each of her strategies. So it's her mixed strategy that must make me indifferent. As such, we need to calculate a player's mixed strategy based on her opponent's payoffs. If you think this is odd, you aren't alone. It takes everyone a bit of time to get comfortable with.
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  185. This was the last thing I cut from the video! I might do something just on that topic later---ironically, when there is more information about what is happening.
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  186. As someone who did a lot of speech therapy as a child, this means a lot!
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  187. You can calculate best responses like that, but keep in mind that we mostly care about equilibrium. So you really need correspondences to get that to work.
    24
  188. hi there hello
    24
  189. Short answer: I don't think it will mean much given that we have been clear that Ukraine was not a "vital" interest whereas there are clear commitments with NATO (and Article V) and Taiwan to intervene.
    24
  190. I didn't sleep much last night.
    23
  191. 75% of it was written and animated before the election. The betting markets had Trump at about a 66% chance to win, so I wrote it with the expectation that he would. Had Harris won instead, I would have flip flopped the second to last and third to last sections and said more about a post-Harris world. It might have taken a couple more hours, but this video was going up one way or another today.
    23
  192. Congrats on first comment!
    23
  193. Zero, and I have been known to on occasion.
    23
  194. Certified first!
    23
  195. That’s very kind, thank you.
    23
  196. Hmm, maybe I will do an “origins of nationalism” video one day. Thanks for the idea!
    22
  197. Update: The location of where Ukraine has been hitting the dam is far less clear than I thought when I produced the video. Don't take the lines I have here as gospel. There is consistency that, whatever exactly Ukraine is doing, it is being precise, and wouldn't be able to target the bridge at all without that level of precision.
    22
  198. Perhaps a more accurate thumbnail would have been "Videos about How Winter Is Coming Are Coming".
    22
  199. You are welcome, Sir First Commenter.
    21
  200. Glad you liked it! Please leave a review on Amazon if you are so inclined. It really helps out.
    21
  201. It's actually titled "Putin Binoculars" because I noticed the Kremlin really likes publishing photos with them, but it long since expanded to a catchall.
    21
  202. Would you believe I waited six months to post this for Janet Yellen to leave office at so that the video would not become outdated?
    21
  203. Yup
    21
  204. Geez, I never noticed that.
    20
  205. It's been a while, and I was getting desperate!
    20
  206. Hard pass on Slochteren!
    20
  207. You mean "Why Every Country _____"? Yes, I was thinking about how to expand the format beyond this one and the NATO one from last year. I was having a hard time of thinking of other good subjects, though. I think EU might work (thanks for that!), but I need to be careful about differentiating it from NATO.
    19
  208. The answer, of course, is "because it was his best response".
    19
  209. Oops!
    19
  210. That would be the right way (using backward induction) to answer the question if the demon could observe your choice. But the demon doesn't observe your choice, and so they can't directly respond to you selecting blue by picking green.
    19
  211. The short version of it is: Ukraine can't credibly tell the U.S. how much they need. (The answer will always be more.) But they can, under some circumstances, say what type of things they want. (Because it will determine what the U.S. gives, and both the U.S. and Ukraine want to push things furthest to the right they can holding fixed some quantity of aid.)
    18
  212.  @alex_zetsu  It seems they are only present when it is cold. I couldn't find them in 2020, 2019, or 2018, and the photos from those parades looked like pleasant weather. I guess the rule is don't have blankets if they are necessary, but if they are, do it on theme.
    18
  213. Nope, never
    18
  214. Consider the break to be a credible signal that I only want to post things when I think I have something useful to say. 🙂
    18
  215. Excuse me sir, but those would be "Lines on Raps"
    18
  216. That paper is a fun combination of abstract math and fixed point theorems. Really important and really interesting, but not worth reading unless you have had the background classes.
    18
  217. Huge if true.
    17
  218. They clearly agreed that fighting was inefficient, and that a negotiated settlement would be better for both parties.
    17
  219. Well that's an interesting first comment.
    17
  220. That's my actual voice. AIs don't breathe audibly into the microphone. :)
    17
  221. Is "you have x% chance of NOT having cancer" any better?
    17
  222. That’s amazing. Do you know a source for it?
    17
  223. That's a legitimate alternative.
    17
  224. Ryan George references are tight.
    16
  225. Did you ever hear the Tragedy of Darth Plagueis the Wise?
    16
  226. Mike Fladlien Thanks!
    16
  227. Two. The full game is always considered a subgame. The other subgame is Firm 2's move.
    16
  228. I see what you did there...
    16
  229. I call unequivocally state that I do not enjoy reaching that dilemma on a regular basis.
    16
  230. I see what you did there.
    16
  231. Love your certified first comment!
    16
  232. JaketheBakedSsnake Given that I've been doing that all my life, I sure hope so!
    16
  233. By not having any fun! If Iran could not hit Israel this weekend, I would be so happy...
    16
  234. Either one could be what the individual meant. The meaning is ambiguous.
    16
  235. Here’s the video: Russia's Declining Oil Capacity and the Deeper Problems of Cartel Politics https://youtu.be/g3VoqnfVJYc
    16
  236. I am The Game (Theory).
    15
  237. thank you for watching today
    15
  238. Weak dominance is very tricky. The videos at the end of this chapter get to it. Remember, though, that Nash equilibrium requires a player to not have any profitable deviations; indifference is okay. That's why there are four pure strategy Nash equilibria here and not just one.
    15
  239. It’s a one-man production
    15
  240. It doesn't need to! You may very well be right. I'm just drawing the lines in ways that are convenient for the visualizations. I don't think there is actually much point in trying to get them "right-right" because the people who can actually do that have access to a ton more information than us. The key question is how much does mud cause power to shift? If there is enough separation between the two sets of bargaining ranges (with mud and without mud), then we are in trouble. If there isn't that much, then we don't have to worry about the upcoming time horizon.
    15
  241. +Toby's Vids Thanks! I say this a lot, but I'd really appreciate a review over on Amazon. It helps out authors a ton.
    15
  242. Mostly what people would call “rational choice security” or “conflict processes”.
    15
  243. 8:53 Saving the best part for the end, it's LINES ON MAPS.
    15
  244. I might after yesterday. Just don’t have the bandwidth for much at the moment.
    15
  245. Game theory is really great for organizing ideas.
    15
  246. Thanks! The videos are 100% me.
    14
  247. Here's the quote from Thatcher. Take it for what you will. "'We can't let this go.... Otherwise, what would happen to Gibraltar, Belize and to other similar places?''" https://www.nytimes.com/1982/04/22/world/iron-lady-displays-gift-at-reception.html
    14
  248. Certified first!
    14
  249. I also have mixed feelings now that the channel has become popular. (Or more accurately mixed feelings about why it has become popular.) Turkey is just looking for a concession, and they will get it. The Baltics are super important strategically. NATO now flanks Kaliningrad because of them.
    14
  250. The previous video blew up, so I will likely do at least one more of these, and more if a war actually starts.
    14
  251. Massively open online course. It was a big buzz phrase three or four years ago that has since died out. #honestanswers
    14
  252. à votre santé
    14
  253. You know you've been watching this channel for too long when you've seen this story four times already.
    14
  254. ***** Nash showed that such equilibria exist for a broad class of games, which is what's really remarkable.
    14
  255. :hug:
    13
  256. Canada and Japan are the most capable of non-weapons states by the measure I created, so that is not far from the truth.
    13
  257. Well, that's a certified first comment!
    13
  258. Look, I'm not exaggerating when I say the success of your mission hinges on how you use that cardboard box. But in the end, a cardboard box is only made of paper. Handle it with care or it won't be of much use to you. Don't think of it as just another box.
    13
  259. Check for mixed strategies
    13
  260. How bizarre!
    13
  261. I can hereby attest and certify that you are indeed first.
    13
  262. I actually won a game of bingo in the fifth grade.
    13
  263. First!!!!
    13
  264. *so far
    13
  265. Thanks so much! I'd really appreciate a review on Amazon when you're ready.
    13
  266. Please don’t I want my viewers to still be alive at the end of this one.
    13
  267. Yep! If anyone else sees this comment and wants to learn more, I recommend this article: https://www.bloomberg.com/graphics/2022-crypto-luna-terra-stablecoin-explainer/
    13
  268. Welcome to the wonderful world of alliance entrapment! (This is a big part of why NATO often has a requirement for applying members to resolve their existing disputes before joining.)
    13
  269. The unfair answer is "because that's not what the statement said." A more helpful answer is passing a driver's test does not guarantee having a license---they might have failed the vision test or been ticketed for a DUI and had their license revoked.
    13
  270. Well at least you struck first blood on the comments!
    12
  271. trust me bro
    12
  272. But what happens if you add Alexander Lukashenko in the mix?
    12
  273. Distinguished viewers, we've got LINES ON MAPS starting at 6:01.
    12
  274. Thanks. I didn't realize that I had the first two in the script rhyming until I said them, and then I stopped recording and rewrote the script to do the other two.
    12
  275. This is one of the things that gets lost when transitioning the math to a more visually appealing medium. All of the claims from papers I have made in this series assign values for the good at stake and then payoffs for proposed divisions. So, to answer your question: yes, the quality matters, and a more precise way to describe the divisions is the expected equivalent valuation of what war would produce.
    12
  276. That is...odd.
    12
  277. Sure, maybe 30 BBY. But 10 BBY? Had to be common knowledge by then.
    12
  278. That's really interesting, and it all makes sense within the context of the incentives. Stealing credentials is an automated process, and the way scammers monetize the information is to sell in bulk. So the goal here is to obtain the most passwords possible without any other considerations, which means making the scams as believable as possible.
    12
  279. Voting "no" could be used as an effective punishment strategy in a larger game in case the other player does something not-so-nice.
    12
  280. Verified first comment speaks the truth.
    12
  281. Certified first comment!
    12
  282. This will increase the cost of producing jerseys and risk pushing the world into an economic downturn. If he cares about extraneous metrics (like lifetime jersey sales), I would say it is bad news! On the other hand, large market teams like the Los Angeles Lakers can absorb recessions better than small market teams. If LeBron wants to stay in LA for the rest of his career, I would say that it would marginally increase the chances of further championships.
    12
  283. Just spread the word! (Orrrrr...you can also check out the books that I have on Amazon.)
    12
  284. Hey, I think you are somebody.
    12
  285. Thanks! This one is extremely popular, so I might do a follow up like it next week.
    12
  286. The derivative is increasing, but the fact that it is negative tells you that the original function is decreasing. (The derivative increasing tells you that the function is convex.)
    12
  287. Game theory is just a way of thinking. Once you have the basics down, you can apply it to any strategic interaction.
    12
  288. Certified first comment!
    11
  289. 7:25 It's not 16 factorial, just in case you were worried about that.
    11
  290. It’s my punishment for declining their nomination for President of the United States. Also, certified first comment.
    11
  291. Certified first!
    11
  292. I like your comment. (It's also the first comment.)
    11
  293. Lines in the video, and the first comment goes to you as well!
    11
  294. +jvgama Yeah, that's basically what I teach my students. The cutpoint for grim trigger gives the minimum threshold of the discount factor to generate outcomes that aren't the reversion outcome (i.e., mutual defection). So if you can use comparative statics to find what changes make that minimum go up or down, then you have some empirical leverage. But this is a lot weaker (and a lot noisier if you try to take to data) than a clean comparative static that says "x is increasing in y."
    11
  295. Verified first!
    11
  296. Thank you for your viewership!
    11
  297. Maybe, but it's been out of sync for a long time already without there being a true crisis. There are also a lot of proposal to expand permanent membership: https://en.wikipedia.org/wiki/Reform_of_the_United_Nations_Security_Council#Permanent_member_proposals
    11
  298. It’s just me. Listen for the breathing.
    11
  299. Why not both?
    10
  300. Certified first comment!
    10
  301. This beats all of the other comments about the hot singles in my area.
    10
  302. In-N-Out is the name of a restaurant. "I eat In-N-Out" is like saying "I eat McDonalds."
    10
  303. Funny you should mention that, my next video is about optimal strategies in the Cones of Dunshire.
    10
  304. Try my Udemy game theory course. There are a few quizzes that take examples from the textbook.
    10
  305. The others basically nailed it. It was a really bad miscalculation on Russia's part.
    10
  306. Certified first one, no less
    10
  307. Hi there hello Sir First Commentor
    10
  308. Certified first!
    10
  309. Apparently he has been skipping sleep during the war, but he sure as hell isn't skipping arm day.
    10
  310. Yeah, secrecy would help in theory. But it is difficult to keep that level of coordination quiet, and there are also problems that come along with it. This may be a long-term plan for a video because there is research on that subject as it relates to nuclear weapons.
    10
  311. And you get a Star Wars reference in the video. Sorry about not having the high ground, btw.
    10
  312. This is basically that topic: https://youtu.be/Sj9cN9yy00U
    10
  313. Interesting, I also just won $1 million playing golf.
    10
  314. Players maximize their own payoffs. If the goal of the game were to outscore the opponent, this would already be reflected in the payoffs.
    10
  315. I don't know. Do I have a dominant strategy?
    10
  316. I am well aware of the origins of the photo. The problem is (not surprisingly) there are not ample free-use images of Russians marching on the streets in protest, so I have to use what is available.
    10
  317. That just makes it a repeated prisoner's dilemma, which is what the last slide was alluding to.
    10
  318. Thanks, and congrats on the first comment!
    10
  319. And actually both of those views were mine. :)
    10
  320. Oops!
    10
  321. Okay, but we’re going to the ice cream shop, right?
    10
  322. Best to make a poll and leave it up to viewers to decide 😂
    10
  323. I am currently reading "The Russo-Ukrainian War: The Return of History" and enjoying it.
    9
  324. Certified!
    9
  325. The dog just sniffs around rather than going through everything. (My car was full of stuff...maybe it is worth re-doing this one to make that point.)
    9
  326. K-9 = canine = dog. So, it's basically a police officer with a dog that has a good sense of smell. They make his toys smell like drugs, gun powder, and explosives, so he gets really excited when he smells something like that, thus alerting the human controller that there is something illegal nearby.
    9
  327. That's what I tried doing with "the 12 causes of war": https://youtu.be/pBwT-5z9R5A I'm also working on a book that takes that video and goes further. Hopefully I will have more on that to share in the upcoming weeks.
    9
  328. Yes, you get the yellow one.
    9
  329. Certified furst!
    9
  330. There are circumstances where offering $20.02 can ultimately be detrimental. Imagine the other guy bid $20.01 instead of $20. You still win and pay the second highest price. But that means you pay $20.01 for a good you only think is worth $20, leaving you with a negative profit.
    9
  331. Do you know the ten chances trick? Every now and then they allude to it, but every prize ends in a 0.
    9
  332. Nope. I have put this in polls for potential videos for the last couple of months, though, so it might sound familiar.
    9
  333. Certified first!
    9
  334. Glad you enjoy it!
    9
  335. Yes
    9
  336. It took four seconds for this comment to be wrong. :)
    9
  337. Thank you!
    9
  338. I think that is the most generous donation I have ever received. Thank you so much!
    9
  339. The first view is always mine, so you definitely got in there right at the beginning!
    9
  340.  @thebugguy6397  I thought I already had. Thanks for letting me know!
    9
  341. That data are only from the post-Napoleonic era. I suspect the average length of wars before that time was longer, in large part because it took forever for troops to get from point A to point B.
    9
  342. Ha, yeah. We could have yet another level of decision making to ask whom the captain is best off delegating the task to.
    9
  343. Ugh. You're right. Not sure why I didn't notice this myself. I will have to upload a corrected version when I get a chance. Thanks.
    9
  344. Change the payoffs and solve for the new equilibria. Good practice! =)
    9
  345. The stoplight just tells players what to do. We don't have to follow it if we don't want to. The point is that we should.
    9
  346. Vacuously true statements often lose coherent meaning precisely because of the vacuousness. For your example, let H you finished your homework and V represent you can play video games. So H => V. Suppose ~H. Then there is no direct relationship between the homework not being done and being able to play video games. You may very well be allowed to play video games--perhaps you need your math tutor to finish your homework assignment, and he isn't there currently. Or you might not. So, really, the implication is asking you to think about a counterfactual world. If you really had finished your homework, would you be allowed to play video games? If the answer is yes, the implication is still fine. If the answer is no, the implication is false, since it claimed that fulfilling H means V is fulfilled as well.
    9
  347. Praise be!
    8
  348. Fourth!
    8
  349. Certified first comment!
    8
  350. But subscribe? :tear:
    8
  351. It depends on the would-be protester's preferences. If they have no interest in protesting no matter how many people are going to show up (but prefer that others do to free ride on the revolution), then that's a large-scale prisoner's dilemma. If the individual actively wants to participate given enough safety from others being there, then it's a stag hunt.
    8
  352. Nice argument!
    8
  353. First person to comment on it, well done!
    8
  354. Certified!
    8
  355. Certified first, actually.
    8
  356. That's a fun fact! Feels like a Final Jeopardy clue.
    8
  357. You, sir, are a scholar.
    8
  358. That's not you being a stick in the mud, that's me being dumb.
    8
  359. Hello, Sir Certified First.
    8
  360. Please leave a review when finished. Thanks!
    8
  361. This confused me a bit when I was first learning game theory. What you have described is non-transitivity of the best response to another player's strategy. A player's preference over outcomes in RPS (win, draw, lose) is transitive, and the preference over outcomes is what matters.
    8
  362. The opposite of that, in fact!
    8
  363. +treeman258 By "very well" I meant in comparison to other strategies. You are right that an accident results in the 4 1 4 1 alternation, but: 1) That's still better than what would happen with a grim trigger strategy. 2) Another accident can bring them back to mutual cooperation. 3) Strategies that never cooperate do extremely poorly. Combine those factors together, and you still circumstances that would make tit-for-tat fare comparatively well.
    8
  364. Second, sadly!
    8
  365. That is often how I feel about them too, haha.
    8
  366. Second, sadly. :(
    8
  367. Fixed it, thanks!
    8
  368. Nice reference!
    8
  369. Short version is that 1) signatories didn't really get a say in whether the five countries had nuclear weapons, as those countries had already made that decision 2) signatories get paid off for not proliferating More on the second bit on the unit on bargaining.
    8
  370. Nothing at the moment. I think what is happening there right now is interesting, but I do not have anything interesting to say about it.
    8
  371. Apologies, everyone! "Why Does Everyone Think They Are an Above Average Driver" won today's poll by a landslide, but I am publishing this one today because it is a little more time-sensitive. Bad driving will come out on Monday instead! Speaking of landslides, private information about risk of landslide is another problem when purchasing a house...
    8
  372. No, but now that I see it I can't unsee it.
    8
  373. I'm animating a spicy one at the end of a video on coups. Should either be the end of next week or the beginning of the following week.
    8
  374. Yeah, I had the same thought when I first saw the game. I will likely do a follow up where the payoffs are solely determined by the number of marbles in the hider's hand. (So if the guesser guesses incorrectly, the guesser has to give that number to the hider.) You still get a hint of dominance, but the reason is much more nuanced, and the equilibrium isn't a simple 50/50.
    8
  375. I was nodding off while editing the video on this one, so right there with you boss.
    8
  376. https://youtube.com/watch?v=vNN4RYXf06c
    8
  377. I made the numbers up. For now, the important feature of payoffs is the rank ordering of the outcomes, i.e. I prefer going first to going second to having us both sit there to causing an accident. The payoffs I used reflect that ordering. Later on (third unit), we will generalize payoffs as variables and investigate how changing the payoffs (while still preserving the rank ordering) affects Nash equilibria.
    8
  378. Yes. For example, for three players, you can draw two matrices. Player 1 picks a row, player 2 picks a column, and player 3 picks the matrix. For four players you can do the same with two sets each consisting of two matrices. Player 4 picks the set.
    8
  379. Moreover, first for the algorithm.
    8
  380. If the other player is mixing according to the equilibrium, then you are stuck earning 2/3 no matter what you do. This is the point of the mixed strategy algorithm, and you cannot improve your welfare unless the other player changes his strategy. The result is inefficient. But there is no requirement for efficiency in equilibrium--we know this from the prisoner's dilemma and stag hunt. Equilibrium just means individuals cannot change their individual strategies and do better.
    8
  381. Given that they appear to be our new T20 overlords, I'm glad I got in on the ground floor.
    8
  382. At the risk of sounding slightly like your lecturer, I do applied research into bargaining and war. Game theory is really useful to keep the logic of your argument straight and prove the existence of agreements that two states prefer to war. I also do research on baseball while I am bored. Check my website.
    8
  383. Y not be the certified first comment?
    8
  384. Well "Kid Rock" is here was not a comment I was expecting.
    7
  385. Third!
    7
  386. Second!
    7
  387. Certified first!
    7
  388. Second!
    7
  389. Whoops, should be 9/15ths and 6/15ths!
    7
  390. That's the precise point--you can't explain the war purely as a result of fictionalization for the exact reasons you laid out.
    7
  391. Give me 15 minutes
    7
  392. It's just a stock image that I have saved in a file. Nothing super meaningful, but time comes up so often in the scripts that it helps to have a default to go to.
    7
  393. Well, that's the very long form video that's going to be after the Strait of Hormuz...
    7
  394. And a verified first comment! :)
    7
  395. Once this course ends, I might edit the overview lecture and add a section on predicate logic. (It is important for game theory.) But that's a long way down the road.
    7
  396. I can understand that perspective, but it is a common notation. It's a pun---pi is representing a "pie" that the parties are bargaining over. The 3.141 value of pi is almost never used in game theory either.
    7
  397. Certified second!
    7
  398. A bunch of people had the same comment the last few videos, and I actually tried picking up the pace in this video. :) The funny thing is that I talk way, way faster in real life. For years, the modal comment about speed on my channel was that I needed to slow down. But perhaps there has been a bit of an overcorrection, and I will keep that in mind going forward.
    7
  399. +vincentyification http://courses.ucsd.edu/rgrush/logic/3-proofs/PS06/ps06_suppl.html
    7
  400. You won the race! First comment.
    7
  401. Thank you!
    7
  402. Hmm. I haven't thought about doing something abstract like that, but it would interesting!
    7
  403. Hi there hello Sir First Response to First Comment Comment
    7
  404. I hope so too...
    7
  405. Distinguished viewers, we have found today's champion!
    7
  406. Thanks! I try.
    7
  407. My computer has a hard time rendering the Google Earth videos that go across the European continent. I shutter to think what would happen if I try having it go across the entire world!
    7
  408. Was I that obvious? 🤔
    7
  409. +treeman258 That's a fair question, but it doesn't change the fact that (no, no) is a Nash equilibrium. "But it's a stupid equilibrium because no would be hurt by choosing 'yes' instead." That seems to be a good point, but in a later lecture I will show that if you don't believe that the (no, no) equilibrium is plausible, INEFFICIENCY results.
    7
  410. Certified first!
    7
  411. Hola hola
    7
  412. Whoops. 3.5 bottles of tequila should go from Mexico to California.
    7
  413. Glad you liked it! I'd really appreciate a review over on Amazon if you could.
    7
  414. This one might be a little basic, but let me know what you think. I have a bunch of ideas for more complicated versions of raffles but wanted to start off simple. In the future, I am going to explore: 1) What if you buy your tickets, I see how many you have purchased, then I buy mine? 2) Same as (1), but imagine it costs me some amount of money to travel to the raffle house. 3) Same as (2), but now the raffle house can charge me a price of entry. What is the price of entry that maximizes the house's payoff?
    7
  415. I’m in the middle of my first play through of it. I’ve enjoyed the dungeon design. Hoping to finish the game on Wednesday.
    7
  416. The model is robust to that. c_A and c_B are A's and B's expected costs of war, which could be greater or smaller than what would actually be realized if they fight.
    7
  417. Yes!
    7
  418. I HAVE NO IDEA. But 7:00 is looking really good right now.
    7
  419. Cool! I am doing a massive update to my gametheory101 website as I type this, including the section on international relations. You might want to check that out.
    7
  420. Phase 3: Profit.
    7
  421. Oopsy
    7
  422. Do you mean the calculus part? Any year-long sequence would work. You just need to know how to do derivatives with multiple variables. The Khan Academy playlist (https://www.youtube.com/playlist?list=PL19E79A0638C8D449) is more than enough.
    7
  423. Finally someone caught this!
    7
  424. Google News doesn’t have a clear number of results returned, so that’s what I had to go with. 🤷🏻‍♂️
    7
  425. I will try my best. It will probably be at the expense of Zuko and his 2.5 seasons of complete idiocy.
    7
  426. Reward process, not outcome!
    7
  427. Nope, there isn't any text for the second half of the course. I've thought about writing it, but there just isn't a large enough market to justify the time expense for me.
    7
  428. The payoff is better for both players collectively, but each individually can do better by defecting on the other one. When the game is finite, this leads to everyone seeing the end game and defecting as a result. This sort of dilemma is easy to solve when you have enforceable contracts, which is something lacking from international relations.
    7
  429. That is a fun fact I did not know!
    7
  430. Thanks for the purchase! I don't think it is too weird. Keep in mind that when x = 0, the goalie can always dive right and guarantee that the kicker does not score. At that point, the striker is indifferent between his strategies and can mix in any way he pleases. This also implies that when x = 0, the equilibrium described is no longer unique. Indeed, in equilibrium, the striker could kick right as a pure strategy, which I think would satisfy you.
    7
  431. The math gets heavier as you go. It’s definitely NOT something like the Russia-Ukraine War book.
    7
  432. You are truly a gentleman and a scholar.
    7
  433. +Jibraeel Khan Durrani You can turn those off bu clicking on the CC button in the bottom right of the video. That said, I'm surprised at the accuracy of the subtitles. They used to be terrible. Google's system has really improved.
    7
  434. Oops, I have been found out
    6
  435. Second!
    6
  436. @Aaron Cobeng If you haven't watched the "12 Causes" video, I do the lines from scratch there. It's intended as an "intro" on the subject. At this point, I try to go through them quickly for new videos.
    6
  437. In interstate conflicts, both states are still around following an international settlement. Thus, both maintain their arms and can revert back to war if the other side cheats on the agreement.
    6
  438. Sorry the audio isn't as good as it usually is. I had to reinstall Windows and I am still working on getting the right filters into place.
    6
  439. My first reaction is: how do we know the public details are exactly what is being sent?
    6
  440. I remember that comment, and thinking to myself that it was unlikely I would. But I found an angle worth talking about, so here we are. Also, you boomed me with the book pivot. Did not see that one coming at all.
    6
  441. Two weeks of actual production, but the research extends before that.
    6
  442. I have angry comments about how I am a Trump apologist, and I have angry comments about how I am a Harris apologist, so this checks out!
    6
  443. That's a clever solution, and better the one that I gave. Some subscribe to the cult of the direct proof. I don't. Sometimes direct proofs make the underlying logic transparent. Sometimes PBCs do this better. So if you have multiple options, think about which one gives the clearer intuition and use that one.
    6
  444. That first bit is a really good intuition for what's going on with your strategy. I wish I had said something like it in the video!
    6
  445. Second, sadly!
    6
  446. Enjoy!
    6
  447. Certified first!
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  448. Certified first comment!
    6
  449. I don't know off the top of my head. Could be an interesting topic for a future video!
    6
  450. Wow, nice catch. Not only to I agree with you, that jacket actually looks like a jacket he wore while visiting the Crimean Bridge following the first attack.
    6
  451. To be fair, the Hiroshima and Nagasaki bombs were two completely different designs. Trinity was the Nagasaki variety. So the U.S. dropped an untested bomb first!
    6
  452. Check back in a couple of videos. The short answer is that if "I run" and "I don't run" were both simple sentences, we could represent one as P and the other as Q. Yet, "I don't run" is the version of "I run" that switches its truth value. (When "I run" is true, "I don't run" is false, and vice versa.) So the cleaner way to represent "I don't run" is with ~P.
    6
  453. +Disaffected Misanthrope I guess all there is to it is that "If Jim, Julia, and Jack are tired" can be broken up into "Jim is tired, Julia is tired, and Jack is tired." We don't say that in English because it's a lot of words. But using "are" is just a shorthand way of saying that all of these things are true.
    6
  454. Who’s there? Nash. Nash who? (Or at least I think that’s where we were on this…)
    6
  455. We are definitely beyond the simple stuff, but most semester-long classes finish with perfect Bayesian equilibrium. So we’re still technically in 101 territory! But not for long...
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  456. !
    6
  457. Thank you so much! Make sure you watch all the way to the end next time. :)
    6
  458. It's a necessary equilibrium condition for the market to all buy from the firm with the lower cost when the prices are the same. Otherwise the lower cost firm could shave its price down by an infinitely small fraction, break the indifference, and profit more from the gained sales than the loss from the lower price. Those strategies aren't an equilibrium either, however, because the lower cost form can always find the middle point between the original price and the shaved down one and profitably deviate. You only get equilibrium when the buyers purchase in that particular way.
    6
  459. Who's there?
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  460. Yes! "Rationality of War" is an introductory text to the subject. This course is what I do for my upper division class on the topic. I am working on a textbook that doubles as the textbook for that class as well as a reference manual for graduate students.
    6
  461. putskan At the risk of answering your question with another question, why wouldn't the player select the equilibrium mixture? She's indifferent between his pure strategies. So choosing 1/3 left is just as good as every other choice. However, unlike every other strategy, picking 1/3 left ensures that player 1 cannot exploit her strategy. That makes the MSNE strategies much more salient than any other strategy combination. For example, if this represented payoffs for soccer penalty kicks (which is an example in a later lecture), not picking the MSNE as a striker would allow the goalie to counter your aiming choice, resulting in fewer goals being scored. Picking your MSNE strategy avoids that.
    6
  462. As the #3 wheat importer, yep!
    6
  463. Thank you for that incredibly generous donation!
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  464. This guy gets it.
    6
  465. Sorry! Didn’t want to get too far off on a tangent. But here is a good explanation of the difficulties of stealing control of a nuke, assuming NM could somehow find soldiers loyal to the governor: https://www.popularmechanics.com/military/weapons/a29576180/us-nuke-theft/
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  466. Certified first comment!
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  467. Third, sorry!
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  468. Third :(
    6
  469. Adding extra cents to your reservation value can't help you but it can hurt. Suppose you valued the good at $20 and you and another person bid $20. Then you either don't receive anything (worth $0) or you receive the good that you value worth $20 but pay $20 ($20 - $20 = $0). Either way, you don't profit. Increasing your bid to $20.02 guarantees you win the good at the second highest price, which is $20. But, again, you still ultimately receive $0.
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  470. Second ain’t bad
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  471. I did a pretty deep dive on that type of mechanism a few videos ago (see below), so I did not cover it so much here. It is hard to balance between “here is one thingI really want to focus on today” and “but there are a ton of other possibilities and none of us as outside observers really know.” It is my focus on the former (for conciseness reasons) that may be why it seems I don’t talk about private benefits enough. Russia Is on a Risky Offensive. Will It Backfire? https://youtu.be/l9XFkn1sPME
    6
  472. Certified first!
    6
  473. I update a handful of lectures each time I teach it. This semester has been a bit more because of coronavirus.
    6
  474. Atomic bomb is a catch all term. A hydrogen bomb is a more powerful type of atomic bomb. More here: https://www.youtube.com/watch?v=OtcC_VJprGQ
    6
  475. Chrisank!!!!!
    6
  476. Confirmed as the official first comment!
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  477. Your timing with the certified first comment certainly did not fall off!
    6
  478. Thanks!
    6
  479. +Adam Smith The assumption is a bit less restrictive than that. For example, you would still be able to generate the same expectation if you could accurately estimate the other's payoff within a certain window. (I think plus/minus .5 works in this case.) Really, you just need to be able to accurately know how the other player ranks each of his outcomes, and you can even fudge this a little bit too. If you can't do those things in the situation you are looking at, then you are entering the world of incomplete information game theory. And you can't begin to study that until you fully comprehend how complete information game theory works. So think of this as a building block to get to empirically richer topics.
    6
  480. Next video: Is Putin Actually an Alien from the Planet Xebes?
    6
  481. You have no idea how much of a problem this is for the game theory subreddit.
    6
  482. Cheers!
    6
  483. hehe...
    6
  484. Nothing specific, it is just a recurring topic on this channel. Here is an analogy. If a mechanic explains to me how an engine works, I will learn quite a lot. But if the mechanic gives the same presentation to another mechanic, nothing will be learned. It would therefore be rather silly if the first mechanic thought that giving the presentation would be informative to that audience. A fair bit of political analysis commits the same fallacy.
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  485. Third, sorry!
    6
  486. The "dilemma" is that cooperating with each other is better than being mean, but being mean is actually what happens. I agree that there is very little actual dilemma here precisely because of the dominant strategy. The stag hunt is a better example of an actual dilemma.
    6
  487. The huge bill is the $3.99 textbook. ;)
    6
  488. Yep, first view is always mine!
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  489. You would think so (and I definitely did not too long ago), but the stability-instability paradox means that this isn't exactly clear cut. International Relations 101: The Stability-Instability Paradox
    6
  490. And certified first comment!
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  491. Certified first comment!
    6
  492. If I use a mixed strategy, I am creating a lottery over outcomes. But lotteries can also be created by non-strategic occurrences, like coin flips or die rolls or colloquial lotteries.
    6
  493. I UNDERSTAND THE REFERENCE
    6
  494. No, game theory is the study of games. The prisoner's dilemma is one such game.
    6
  495. It can go both ways! The size of the "cost" line is determined by two things: the physical costs and how much the actor cares about the situation. Seeing atrocities might make Ukraine think that first part is larger than they anticipated, but it might also make them care more. The net effect is nebulous and depends on which is the stronger effect. You can see more about how those are formalized here: https://www.youtube.com/watch?v=w9CwkQK3Tc4&list=PLKI1h_nAkaQrvKPtuPMXkU4yXCDSp_NHh&index=2
    6
  496. It can, but the net effect is nebulous. If I know that you have an incentive to look tough against a third state, it can also result in me making greater concessions to you to avoid war. Essentially, I "buy out" your incentive to act tough. In other words, having a third party observing the outcome of the first conflict can either increase or decrease the probability of war. (That's also before you start thinking about how war right now would hurt a state's ability to wage war against the third party, which further suppresses war in the first negotiations.)
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  497. That will be the next video I produce! Something else may appear between now and then but only because it is already done.
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  498. First comment, nice
    6
  499. That is incredibly generous! Thank you so much.
    6
  500. Gotta keep the special relationship intact!
    6
  501. Good luck!
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  502. 100% new
    6
  503. Podcasts would be much faster to produce than these videos, but won’t have the same reach. It is something I will consider as my base audience grows.
    6
  504. Thank you! That was very generous.
    6
  505. Thank you!
    6
  506. (Pub, hare) and (stag, stag) are the game's PSNE. (There are more in mixed strategies.) Player 1 cannot hunt a hare in any equilibrium because choosing pub strictly dominates it.
    6
  507. To be willing to mix, you have to be indifferent between your pure strategies. Your opponent's randomization causes your indifference, which in turn makes your randomizing rational. Check back to the mixed strategy algorithm video for the logic.
    6
  508. The "agreement" beforehand is substantially less important than what the people actually want. The prisoners in this example could "agree" to keep quiet before the interrogation, but each individual would want to break it as soon as the policeman makes them the offer. In contrast, if we both most wanted to get along with each other, than cooperation is easy. From a war perspective, the US wouldn't want to play mean against Canada because we like Canada. Same would not be true with US and Iran.
    6
  509. +Disaffected Misanthrope Respect.
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  510. Certified first!
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  511. Game Theory 101, my friend!
    6
  512. There’s an entire playlist on that: Bargaining and War Full Course https://www.youtube.com/playlist?list=PLKI1h_nAkaQrvKPtuPMXkU4yXCDSp_NHh
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  513. Random reply for engagement purposes.
    5
  514. I also have an example in the textbook about the split or steal/friend or foe game.
    5
  515. International Relations 101: Nuclear Pessimism
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  516. First indeed!
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  517. You get the same solution through iterated elimination of STRICTLY dominated strategies but not through iterated elimination of WEAKLY dominated strategies.
    5
  518. Good question. Two reasons: (1) There is good reason to believe that states should act rationally unlike individuals. Of course, this is just an assumption and might not always apply, but I talked about the justification for it in the first chapter. However, (2) there is much less incentive to cooperate in this game than there is in the centipede game. The centipede game has the overall size of the "pie" increasing every time someone passes, while the "pie" remains the same size here.
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  519. Certified first!
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  520.  @dualtronix4438  If something happens, yes. If not, I have discussed the issues with it enough before that I do not have anything new to add. If the drama continues for long enough, then I will accumulate enough new material to warrant an update.
    5
  521. I had to look this up before producing the video---I would have guessed that it violates the rule. It turns out that Armenia doesn't have a McDonald's, though.
    5
  522. Second!
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  523. Thanks!
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  524. I 100% understand your sentiment. If 90% of viewers were returning, I would be inclined to do what you suggest. However, returning viewers are typically make up less than 50% of the audience. If I stopped to say "hey, watch this video if you don't understand what's going on here," one of two things would happen: (1) some viewers would do that or (2) viewers would get confused and then just click off. Either way, the YouTube algorithm won't be happy, the video won't circulate, I won't get any revenue, and I'd be better off focusing my energy elsewhere. In sum, I agree. But that's not how this platform works, and I am at its mercy.
    5
  525. Well, I did mention at the end that I was traveling across the country. Just about everything I owned was in the car. It was packed to the top.
    5
  526. Prisoner's dilemmas are commitment problems (you can't commit to cooperation). Collective action problems are prisoner's dilemmas with lots of players (instead of just two). Thus, collective action problems are commitment problems. (But not all commitment problems are collective action problems.)
    5
  527. There is a deeper issue that prevented the sides from bargaining, which we will eventually get to.
    5
  528. +Howard Ackerman You'd have to solve it as a standard system of equations. Pesky algebra strikes again...
    5
  529. Yes, it's an assumption. This is literally the simplest model of conflict and cooperation you can create. We'll be doing the "real" model of war in the next chapter. Interesting spoiler: even if peace is better than easy conquest, you can still get rational war.
    5
  530. What we "know" almost entirely comes from laboratory experiments in which people (normally college students) are offered money to play a game. This is a vastly different exercise from participating in a real life transaction. Yet, from these experiments, we also know that the evaluation of "fairness" rapidly becomes irrelevant as the size of the stakes increase. In other words, people are willing to inject a lot more fairness into the equation when $1 is at stake versus $100. In many ways, bargaining in the shadow of war is the largest stakes you can create. Regardless, if you were to add some evaluation of "fairness" to the model, it remains true that the proposer offers no more than what is necessary to induce compliance. Indeed, you can account for this fairness by simply reducing the cost of war. So instead of thinking of cR as the rebel's cost of fighting, you could think of it as its cost of fighting and a valuation of fairness. In any case, G still offers x = pR - cR and R accepts. Part (b) is only true when there is incomplete information in the interaction. Repeated interactions do not change the result with complete information. As mentioned in the lecture, incomplete information is a topic for future lectures.
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  531. Just trying to make sure all those unemployed lines on maps can get a job. It's important in this economy.
    5
  532. Thanks. This is for my class, and I like to leave them unsure of my true political leanings by the end of the semester.
    5
  533. "Can I set up a strategy steal" is always a good place to start!
    5
  534. No, just taking an end of the year break!
    5
  535. Certified first comment!
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  536. I have a couple. Second price auctions: https://www.youtube.com/watch?v=VUN-k_nfDts The winner's curse: https://www.youtube.com/watch?v=DkdiZr008HY No plans for anything in the future. I am a political scientist, not an economist, so auctions aren't my thing.
    5
  537. In my opinion, I talk a little slow too. :)
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  538. +starrychloe You can. There's nothing wrong with that, and it will always produce independent preferences---for this lottery or any other setup.
    5
  539. +Joshua Howard You, sir, are the worst kind of Mario Kart player.
    5
  540. Yes, terrorism and insurgency will be the third part of the class.
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  541. +Inventive Harvest That preserves the ordering but will mess with the mixed strategies. You can try it with a game that has an MSNE, or just think of the preference over 1/4 with certainty and a lottery between 0 and 2 and compare that to the preference over 1/16 with certainty and a lottery between 0 and 4. There are infinitely many other ways to preserve the ordering (for example, u^n, for all n odd), but only positive affine transformations preserve the preferences over lotteries as well.
    5
  542. Second!
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  543. Welcome to the fun world of the YouTube algorithm!
    5
  544. It is, thanks. Just been prioritizing getting tenure!
    5
  545. Thank you for the first comment!
    5
  546. I talk more about the meaning of the payoffs in lesson 1.1 of Game Theory 101: The Complete Textbook. You should check that section out. (It's in the free sample Amazon provides, so you should do this regardless of whether you want to buy the book.)
    5
  547. +johnception Not in a one-shot game. Nash equilibria checks for that kind of thing. If the game were repeated many times, then the story might be different. But repeated games are a much different beast covered later in the course.
    5
  548. abc6450 Depends on where you go for undergrad/grad, but some do.
    5
  549. Thank you!
    5
  550. 10:42 LINES ON MAPS. Also, I am thinking of starting a new game: count the number of times Sergei Shoigu shows up in the Kremlin's photos.
    5
  551. I was beginning to worry no one noticed it!
    5
  552. Indeed!
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  553. Certified first!
    5
  554. Those assumptions sound similar to the incomplete information case we will look at later.
    5
  555. In principle, yes. Whether it is the first player or second player that can do, I'm not sure off the top of my head. But it wouldn't be difficult to expand the same solving strategy to a third dimension. Actually, I have thought about doing just that in a future video. The problem is that I don't think there is a visually pleasant way to do it.
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  556. The melt traps appear to be missing from ZNPP's designs. See page 26: https://network.bellona.org/content/uploads/sites/3/2023/06/The-Radiation-Risks-of-Seizing-the-Zaporizhzhia-Nuclear-Power-Plant.pdf
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  557. A little bit of column (a), a little bit of column (b). Here’s the best explainer of the problems with stealing a bomb that I could find: https://www.popularmechanics.com/military/weapons/a29576180/us-nuke-theft/
    5
  558. Seventh, sadly. :(
    5
  559. Thanks for all your comments! They are great. The course is designed for political scientists (of which I am one), so the science part of the class is lacking depth. Could you email me if you have a chance? Thanks.
    5
  560. Yep, bullets flying into and turning on bullet-making machines.
    5
  561. The primary system encourages politicians to adopt party medians during the primary. But note that immediately following primaries, candidates normally rush right back to the middle.
    5
  562. Actually, there is a ! reference in this video...
    5
  563. !
    5
  564. Modern problems require modern solutions.
    5
  565. +SupermarketSweep777 Alternatively, you could say to hell with it, and go on Supermarket Sweep instead. It's the better game show anyway.
    5
  566. https://www.youtube.com/@LinesonMapsExtra
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  567. Yeah, I could see how that’s a problem. The other one had a mechanic where if you hid in one spot, you would automatically lose some portion of the time. In this one, your opponent might fail some portion of the time if they pick correctly. These sound similar on paper, but it turns out that the other problem is substantially more difficult!
    5
  568. I do research on different expectations of outcomes. I have a couple of pure theory videos on the topic. This is the version for an introductory class: https://www.youtube.com/watch?v=H-4gJMvEF5I&list=PLB5965C13F4B0B2DA&index=21 And a more technical version is here: https://www.youtube.com/watch?v=9DchoR0qw0Y&list=PLKI1h_nAkaQrvKPtuPMXkU4yXCDSp_NHh&index=23 I think I will do a version of this specific to Russia/Ukraine next week. I don't do as much on principal-agent problems (Russia's interest =/= Putin's interest), so I don't have any immediate plans there. If the right thing comes up, though, that might change. Irrationality isn't my research interest at all, so I am almost certainly going to stay out of that.
    5
  569. I wrote and animated that video last week and spent the entire weekend checking whether Biden had already given the go ahead and I would have to rewrite the whole thing.
    5
  570. My syllabus is here: http://wjspaniel.wordpress.com/pscir-265/
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  571. Holy cow, didn't realize this video is from 2012.
    5
  572. Making Penguins fans everywhere cry. ='(
    5
  573. Sorry it’s just how I talk
    5
  574. jvgama That's next lecture. :)
    5
  575. That's correct. The good news is that generalizing risk preferences won't invalidate the broad themes of this portion of the course, though.
    5
  576. +Marko Savic It's exactly the same thing. Remember that the proofs are basically conditional proofs (well, actually, you will get to that later) where we assume that the premises are true and see what follows as well. Put differently, IF premises THEN conclusion. So you have P arrow Q and P as premises ((P arrow Q) ^ P) and have Q as a conclusion. Or ((P arrow Q)^P) arrow Q. Clear?
    5
  577. Certified first!
    5
  578. Indeed it is a branch of discrete math.
    5
  579. I'd stick to $1M. I'm very risk averse.
    5
  580. +Yelena Antipova It doesn't disappear so much as it never gets produced. Had the markets been open, domestic forces would have reallocated their labor in a way that would have produced more stuff. The lost surplus is the absence of that stuff because labor was never reallocated.
    5
  581. That’s be an interesting twist!
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  582. Certified first!
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  583. Possible explanation: this was a MTG channel circa 2007.
    5
  584. I don't know about the result you are talking about, but it sounds like it's the same mechanism. Noisy signals can cause you to get more adventurous in your choices. The additional information is better for you in expectation, but there is also some chance that you take a riskier option that backfires with some probability. This is the result from crisis bargaining. The video is currently unlisted (it is slated for publication in a couple of months) but is available through a direct link: https://www.youtube.com/watch?v=3Yp2rbJaB-M&list=PLKI1h_nAkaQrvKPtuPMXkU4yXCDSp_NHh&index=22
    5
  585. Correct. And best of luck trying to solve such a monstrosity!
    5
  586. William Spaniel: the great demographic unifier* *males only
    5
  587. 126th
    5
  588. Keep watching…cooperation eventually works.
    5
  589. +PIME32 https://www.youtube.com/watch?v=Vy5reCmEfBg&index=20&list=PLKI1h_nAkaQoDzI4xDIXzx6U2ergFmedo TL;DW: If only one thing can happen in the final stage (because there is a single Nash equilibrium), actions in the previous stage can't have any impact on what we will do later. For example, in a prisoner's dilemma, no matter what happened before, defect is always going to be better for me in the last stage than cooperating.
    5
  590. Play defensively.
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  591. It's because player 2 doesn't make her move until player 1 has already moved. Right is not a credible threat in this context, as player 2 would never want to actually go right once she sees that player 1 has moved up.
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  592. Here's a really crude explanation. Imagine there is a giant bag of marbles. 99% of them are black and 1% of them are white. You really only want the white ones, so you reach your hand in and pull one out at a time. Is it impossible to find white marbles? No, but it will take some effort. Now imagine you have a bag that has 80% black marbles and 20% white marbles. It will take substantially less time in expectation to find a white marble. Black marbles here are U-238, and white marbles are U-235.
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  593. Huge misplay on my part here.
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  594. Second!
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  595. Verified first!
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  596. Verified first! (Edit: Actually, this was second. Sorry.)
    5
  597. It’s a challenge because that letter has so many darn syllables.
    5
  598. I was very pleased when I found those!
    5
  599. Thanks! Hope you enjoy it.
    5
  600. There's a lot of stuff in modern international relations that doesn't look like this, but this is so integral to modern research that you really cannot avoid it. The article this model comes from is the most cited publication since its release in 1995.
    5
  601. No, I love this guy. ^
    5
  602. Confirmed first!
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  603. The idea is that if both stop, then they lose a few seconds coordinating who should go first. But you'll notice that (pass, stop) and (stop, pass) are still the only pure strategy Nash equilibria even if make your suggested adjustment.
    5
  604. It really does astound me how having the word “crypto” immediately gets every spambot in the world to drop by.
    5
  605. I sympathize, but the answer is yes. Engagement drops off even if I do daily uploads. Large gaps in content actually result in a spike in viewership for the new video.
    5
  606. Once one thing dominates another, you get rid of the second one immediately. No need to do any extra work. Whether a third thing is better than the second is irrelevant. You wouldn't want to play the second strategy when you could play the first, regardless of what is going on with the third.
    5
  607. Flip-flopped, actually. Ad-libbed the script change when I realized what was in front of me.
    5
  608. Classic rookie error to exclude LeBron from the conversation.
    5
  609. Thank you so much! Very generous.
    4
  610. I saw your comment and saw the popcorn!
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  611. The textbook is super basic, so be careful buying it if you already know a lot!
    4
  612. You’ll be happy to know that, despite the flood of comments on this channel from the last two weeks, YouTube’s algorithm is still sending me alert emails for your comments.
    4
  613. Less trivially, it can come up when a player chooses a variable within the game. It is no longer exogenous (it's endogenous), but for the purposes of the subgame, it is a knife-edge condition. You still have to solve for it, though, because you need to know what happens in the subgame to find the solution the the decision beforehand. This usually requires a lot of work. I had to do one of these proofs for my latest papers, and it sucked.
    4
  614. They come up when someone is in control of the game. If the game in the video were for money and being played in a lab, I could set x = 0 and have you and your friend play.
    4
  615. It's a genuine outtake. I do the animations, and then record audio as I watch the animations. There's usually a couple of animations I program poorly, but I don't realize it until I am narrating. For that one, I wanted to zoom about 105%, and I instead mistakenly set it for 400%. That was my live reaction to getting way, way too close to Zelensky's face.
    4
  616. Thank you!
    4
  617. Certified first!
    4
  618. If I learned anything from Obi-Wan, it's that the high ground is more important than anything else.
    4
  619. I just want to play Echoes of Wisdom 😢
    4
  620. Oh okay let me get off of that thing.
    4
  621. Very generous, thanks!
    4
  622. It’s because pitch meeting quotes are tight.
    4
  623. I can do one where there is no optimal team. Does that sound interesting? Works for soccer, cricket, or whatever.
    4
  624. Second!
    4
  625. I think I would treat this way of solving the problem as "right answer, wrong reason". If I am understanding what you did, I don't think it generalizes to beyond two strategies. It is interesting that you can do it this way, though. I hadn't thought about that before. I am unaware of a full solution to any standard game of poker.
    4
  626. I hadn't thought about this before, but yeah using the value of the cards can simplify how you actually execute the mixing!
    4
  627. One of the more surprising things I have learned over the years is that (many, not all) protestors actually want to be there for the sake of being there if the protest is going to be successful. It's interesting because the desire to participate means that there is no free rider problem (again, at least for them) despite a situation that seems all built up for one.
    4
  628. It is accurate. The mix up may be between nominal figures and purchasing power parity.
    4
  629. Third!
    4
  630. Yep, the generalization to n pirates gets really weird because you start needed progressively (and exponentially) larger coalitions for the captain to survive.
    4
  631. I have that on my whiteboard as a thing to eventually do, but I have no short-term plans for it.
    4
  632. All of your comments are hilarious!
    4
  633. It’s true. I get unreasonably excited when one of the major accounts does a photo dump on Flickr.
    4
  634. That's an all-time great comment right there.
    4
  635. +sinecurve9999 Not anymore! Thanks for point that out.
    4
  636. I have a qualifying paper due Thursday.
    4
  637. Thank you very much!
    4
  638. Hi General 12th!
    4
  639. Glad you like them!
    4
  640. Thanks, I've been working to get better with them!
    4
  641. You can start a conditional proof with whatever you want. When you close it, though, the antecedent of the conditional statement you have just proven (e.g., Line 7 at 6:57) needs to be the first line of the conditional proof.
    4
  642. My university provides 24 hour security. It was part of the agreement for me to come here.
    4
  643. He's a very influential (if controversial) linguist, but I wouldn't think of him as any thing more than a pundit in the realm of politics. Looking back on the lectures, I think the only thing I have taught that is still controversial within political science is the democratic peace theory. Everything else has basically been a proven formal or statistical result.
    4
  644. You need an individual to be able to rank their outcomes from best to worst. Without completeness, there would be a bunch of question marks.
    4
  645. Maybe I am just getting angrier as I get older?
    4
  646. @ZlotDrop You're right. I wrote an article to accompany this video that clarifies that this theory only applies before minions have spawned. At that point, the incentives change and you can't always leave two lanes unguarded.
    4
  647. No, the bonus squares only work the first time you play on them.
    4
  648. No worries, about the edit. You are correct, and I appreciate you catching it!
    4
  649. Game theory allows for individuals to have benevolent preferences. However, they are incorporated directly into the utilities. You can't "double count" once you have already assigned payoffs. Note that the lecture explicitly stated that we are assuming that the individuals only want to minimize jail time. If we didn't, then the game would look more like a stag hunt, which is covered two lectures later.
    4
  650. I never really put forethought into it. I used to label them "cooperate" and "defect" (standard for the literature on the prisoner's dilemma), but then too many people complained that those were confusing.
    4
  651. Yup, that's definitely a problem if the police create this type of incentive structure.
    4
  652. It's in the Washington Post article on it, but it's a recurring theme in the news coverage around the battle back when it was still a fresh subject. https://www.washingtonpost.com/national-security/interactive/2022/kyiv-battle-ukraine-survival/
    4
  653. You are persistent enough that eventually I am going to have to make that work... There will be a Laker referenced in the next video, but it won't be LeBron.
    4
  654. If my consumption of sports media has offered any insight there, the answer is "way too often".
    4
  655. +alittlepenny saidhi I have some caveats. There are MSNE in non-zero sum games. There are MSNE when there are also PSNE. And you can have MSNE when a player has a single dominant strategy. You'll see examples of all of these later in the course.
    4
  656. I actually gave a talk at Buffalo earlier this year. (Poli sci, not econ,) Been there a couple of times so far. Nice place, though I question the usefulness of the solar panels.
    4
  657. Damn homophones.
    4
  658. You are the first comment to notice it. :)
    4
  659. I'm confused. Are you suggesting that I try to become a professor? Cause I'm already tenured...
    4
  660. Thanks, and glad to have helped on the course!
    4
  661. Thank you! And I hope you caught the end of today’s video.
    4
  662. Fourth!
    4
  663. Right, it's hyperbole. China holds less than 10% of U.S. debt. Obviously, that does not change the fact that it would be silly to purchase such a large share of a "company" and then try to steal it.
    4
  664. No. Whatever values the players have regarding the other players' outcomes is already reflected in their payoffs. So if it says player 1 receives 3 if he goes up and 3 if he goes down, then he is completely indifferent between those outcomes.
    4
  665. Discrete Cornout: https://www.youtube.com/watch?v=UL6Kv88YXqQ (There's a continuous version in the textbook as well.) Hotelling: https://www.youtube.com/watch?v=THVrl_2Mu1A I am a political scientist, so the economic models of competition don't really interest me.
    4
  666. pallas100 Great! I should be doing this one pretty quickly---one lecture a day, minus weekends and my travel commitments.
    4
  667. Thank you!
    4
  668. An accepted proposal ends the interaction. Other than that, it can continue forever in the sense that you could have an infinitely long (and iterated) extensive form game tree.
    4
  669. Third, sorry.
    4
  670. +TAEHSAEN I'm not sure if there's a better answer than "that's just how conditional proofs work." When you begin a conditional proof, you choose something to assume. Let's call that A. Then you can apply the rules of logical inference as normal. After, the rules of conditional proofs say that you may conclude that A => [ ], where [ ] is whatever you found through the standard proof process. The idea is that the first line assumes that something is true, and the rest of the proof techniques show that other things must be true CONDITIONAL on the assumption that you made initially. Hence you use the conditional operator =>.
    4
  671. Rare is the four paragraph comment that I don’t regret reading! 😅
    4
  672. Thanks! Please leave a review over on Amazon if you get a chance. It really helps out. :)
    4
  673. If a player mixes in equilibrium, he must be indifferent among all strategies he plays with positive probability. He therefore must also have the same payoff for mixing in any way among those strategies. So, the answer is yes.
    4
  674. Thanks! Hope you are enjoying the new content too.
    4
  675. Welcome to the fun world of Google Earth's copyright information not always matching what the images show!
    4
  676. Here's hoping that viewership is a marathon, not a sprint...
    4
  677. !
    4
  678. Ukraine's claim is specifically 17k KIA, 30k wounded. Incentives to misrepresent caveat applies. https://news.yahoo.com/17-000-russian-soldiers-killed-133100810.html
    4
  679. The French name for Switzerland is Suisse. So, it's different, but it still falls in between them (unless there is something further confusing going on).
    4
  680. Nope, they are completely separate groups!
    4
  681. That's actually somewhat common in non-center-seeking civil wars (i.e., those being fought for regional autonomy). If the rebel group is winning, then they might reach some kind of settlement granting limited autonomy. It's much harder to stay mobilized after a peace agreement in a center-seeking civil war (i.e., those being fought for control of the central government) simply because there often aren't clear battle lines.
    4
  682. I do! Wallace, Michael D, Brian L Crissey and Linn I Sennott. 1986. “Accidental nuclear war: A risk assessment.” Journal of Peace Research 23(1):9–27. Lundgren, Carl. 2013. “What are the odds? Assessing the probability of a nuclear war.” The Nonproliferation Review 20(2):361–374.
    4
  683. Success!
    4
  684. I don't have a "real" answer to your question, but here is my guess. As far as I can tell, you are right that the exclusive or is more common in everyday language. However, also as far as I can tell, the inclusive or is more common in mathematical proofs. So that's my guess why OR got that designation and not XOR.
    4
  685. That's correct. There's a lecture on the exclusive OR in the next unit that talks about that.
    4
  686. Ha, no, didn't even make the connection until your comment. I have a bunch of similar games where the winning first move is different, so this won't be a recurring theme!
    4
  687. Nailed it.
    4
  688. Certified first comment!
    4
  689. Second, sorry.
    4
  690. Thanks!
    4
  691. You could.
    4
  692. There's a giant literature on this. I think the most compelling explanation is that the parties don't know exactly where the median voter is. When that's the case, you begin to get separation in policy platforms. I'll eventually do a video on that, but it will probably be closer to the 2024 election before it happens.
    4
  693. +Call4meWT http://people.bath.ac.uk/ecsjgs/Teaching/Industrial%20Organisation/Papers/Hotelling%20-%20Stability%20in%20Competition.pdf
    4
  694. https://www.youtube.com/@LinesonMapsExtra
    4
  695. There are infinitely many equilibria in which P2 plays right as a pure strategy and P1 mixes between up and down.
    4
  696. There are!
    4
  697. You got me there, sir.
    4
  698. @Dexmonicus ...which is technically covered by this game, when V = C!
    4
  699. That’s an actual photo!
    4
  700. Yeah, the mixed strategies are always difficult to eyeball, which spills over into the meta question of what to do with the removal.
    4
  701. +19selena19 That checks out!
    4
  702. Yeah, probably. Oh well! You live, you learn.
    4
  703. Yup, no idea why my video editing software decided to stick that in there!
    4
  704. "Center strictly dominates right" (or "right is strictly dominated by center") is the correct statement. "A strictly dominates B" is a pairwise comparison, and however the payoffs work for tertiary strategies is irrelevant. This can be confusing because "A is a strictly dominant strategy" is a global statement, meaning that A is better than every other strategy the player has. It took me an embarrassingly long time to get my head around this.
    4
  705. About half way through the Fast and Furious franchise, Vin Diesel's character became obsessed with his "family": https://www.youtube.com/watch?v=IQuc7wfO16Q
    4
  706. There's still one more in the series!
    4
  707. Well, you can't define a game in which the other side has no probability of being capable of knowing the information but does so anyway. If there were a very small probability that one type could see the information, then the other player would be willing to gamble that the first player doesn't know which side of the coin is facing up. Then the type that has that knowledge gets a greater payoff than the side without that knowledge.
    4
  708. It's a long bet, you see. In fifty years, the pronunciations of "hears" and "years" are going to drift together, to the point where they become the same word. 🙊
    4
  709. Seems like three separate dimensions. Need lines on cubes at minimum…
    4
  710. That's another A+ comment right there.
    4
  711. abc6450 Yup, he can offer anything at all.
    4
  712. In short, it's basically impossible to establish causation of meaningful relationships in international relations conflict data. (If you think about what the ideal experiment would be to establish causation here, we would have to randomly assign ability to produce nuclear weapons...which has all sorts of practical and moral problems.) What we can say is that the empirical world reflects a hypothesis that the theoretical model predicts. It's also worth noting that the observational relationship described in the video holds after you control for the types of things described.
    4
  713. The voice monotony would put people to sleep. -_-
    4
  714. I can't be sure about what you are asking without a specific time stamp, but I think the trick is 1 - d^2 = (1 + d)(1 - d).
    4
  715. HitomiAyumu Yep! Here's an example: https://www.youtube.com/watch?v=4jNGngVspS8
    4
  716. Certified first!
    4
  717. That's what it will start looking like once we transition to the generalized model.
    4
  718. The first view is always me doublechecking everything. You are actually the first!
    4
  719. Certified first!
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  720. Third!
    4
  721. Not necessarily dead, but no current plans to add to it.
    4
  722. My man here asking the real questions.
    4
  723. If you are playing to maximize marbles over the long run (and not trying to capture the fixed quantity of ten your opponent has, as on the show), the hider needs to place slightly more weight on hiding 9 and slightly less on hiding 10.
    4
  724. I always am in real life. At least the videos give me a do-over if things go too wrong.
    4
  725. I dropped the ball!
    4
  726. FYI: This is only a slightly updated version of the old Selection Problems lecture for this series. I'm teaching the class again this semester IRL and making some alterations throughout the playlist to ensure accuracy.
    4
  727. mariorpg11 >Is the gm just some kind of abstract conzept we need for understanding the theory? This is the correct way to think about it.
    4
  728. jvgama We're going to assume continuity of the goods throughout the rest of the course. This is justifiable in wage negotiations, since $19.995 per hour is better than $19.99 per hour, and the fractions can round over the course of pay periods.
    4
  729. That’s the United Nations in New York.
    4
  730. Oops, you are right.
    4
  731. I hope not so early that YouTube was still showing a washed-out version because the video hadn't completely processed yet!
    4
  732. +Pakki Premkiran Rao No. I can see why someone might think that, but note that you can rewrite line 2 as ~Q v ~Q by conditional exchange. Nothing wrong with there.
    4
  733.  @Fantosofthelight  Ah, okay. In that case, you still do the process at 2:10 to derive the best response. The tricky thing is that the first order condition can be complicated because the derivative of the marginal cost function c(q_1) will have q_1 floating around in it. Thus, when solving for q_1, you are going to have to jump through more mathematical hoops.
    4
  734. That's right. Per the odd rule ( https://youtu.be/RhSaq97YjbA ), there is a third equilibrium, and it is in mixed strategies.
    4
  735. I think you are referring to a theorem for infinitely repeated games, which would explain the discrepancy. In finite games, the strategies in the last stage MUST be a Nash equilibrium.
    4
  736. Third, sorry!
    4
  737. Thanks! But sadly you were second this time.
    4
  738. +Azza Zidi I will be, but not before this academic school year finishes---I have ~9 more lectures of BNE to do, and I also have a cross-country move to plan.
    4
  739. It’s just my voice
    4
  740. It was actually a muay thai knee, but please don't tell anyone!
    4
  741. yam s I would go with Canada for the United States and Germany or the U.S. for the U.K. http://en.wikipedia.org/wiki/List_of_the_largest_trading_partners_of_the_United_States http://www.theguardian.com/news/datablog/2010/feb/24/uk-trade-exports-imports#_
    4
  742. I've uploaded a handful of IR lectures in the last few months---on UN voting, war data, leaders, and now a full unit on sanctions.
    4
  743. One comment and zero views so far. Interesting...
    4
  744. The whole point of [my YouTube channel] is lost, if you keep it a *secret*! Why didn't you tell the world, eh?
    4
  745. I’m not sure those would be inherently more interesting because you can create any payoffs you want using the selfish preferences here. So if you had a game with a payoff matrix that factored in wanting to save the others, you could also do that by just changing the number of animals and maintaining selfish preferences. That said, some altruism makes the problem a little bit harder because there is some extra bookkeeping to do. I have a plan for a future video where there are humans and dogs, and dogs value humans just as much as dogs. And I also have an idea for an interesting comparison to a game’s outcome with selfish versus altruistic preferences.
    4
  746. Certified first!
    4
  747. I don't have anything on multi-item auctions. I will think about whether I can construct one, though, because that seems like an interesting topic. I have this video on second-price auctions, which were for a long time how Google operated the market: https://youtu.be/VUN-k_nfDts
    4
  748. Game Theory 101: The Complete Textbook is the best place to start. After that, I would recommend Game Theory Evolving by Gintis.
    4
  749. You are right that there is a connection between the economy and civil war: states with low GDP are much, much more likely to fight than states with a large GDP. However, I don't think (this is me mostly speculating at the moment) that the 90's recession impacted this, largely because (if I recall correctly) the recession disproportionately impacted countries with high GDP, and they weren't likely to fight anyway.
    4
  750. Certified first, and thank you!
    4
  751. Second, indeed, but the first commenter deleted theirs. So technically yours is now first!
    4
  752. I've done a few of these: Hostomel Airport: https://youtu.be/hh9xT9d6SJU Eastern Counterattack: https://youtu.be/nWv2OY01fOI Kherson: https://youtu.be/WmqIJaTt4MM Battle of Kyiv will be my next long video. There may be a couple of shorter ones I do between now and then.
    4
  753. +For Evermore On the other hand, I love your comment.
    4
  754. Yep, the odd version of the game is much more interesting once you realize THIS ONE SIMPLE TRICK to win the even numbered game. I might do an example of an odd one many months from now if I can construct one that is both interesting and tractable.
    4
  755. So much regret right now. =(
    4
  756. Yeah, it's surprising how much more difficult it gets when even a little uncertainty is introduced.
    4
  757. +ed frank Amen.
    4
  758. "You know what they say about a good Star Wars reference… it can really bring the galaxy together." ^ That is a recommended AI comment YouTube offered me. Yuck!
    4
  759. Hello there!
    4
  760. You keep using that word…
    4
  761. It's a good question. There can be some amount of delay in between the signal of the end of the world and the actual end of the world. Everyone keeps cooperating until they receive the signal, and then they defect until the end. The math is a bit more complicated, though.
    4
  762. +Sashank Ramesh As it turns out, never---no matter how long it is. The interaction has to be infinite. https://www.youtube.com/watch?v=x50rADoxHyc
    4
  763. This one's going to be every Monday from now until it's over. They are all already recorded, so there shouldn't be any disruptions.
    4
  764. Confirmed first comment!
    4
  765. Glad you are still with us!
    4
  766. Not really. Player 2's moves were not limited. Player 2 could have still chosen rabbit. It's just that player 1 has conveyed information to player 2 by not going to the pub. That information makes choosing rabbit a bad move for player 2.
    4
  767. Oh no! I guess it is fitting given that the central problem is that it is hard to tell the two apart. :)
    4
  768. +Maderra -4 No, that would mean that maintaining a $1,000 balance ensures that you won't pay absurd bank fees. The English sentences leave open the possibility that one could have that much in the account but still pay absurd fees for some other reason.
    4
  769. +violinsheets That follows example #4. Think about rewriting it as "Maintaining a $1000 balance is necessary for not paying absurd bank fees." M is necessary for not F. ~F ⇒ M.
    4
  770. I am satisfied, thank you! 😅
    4
  771. Wait until Thursday's video ;)
    4
  772. Depends on the public good. But think about the safe seas example. The U.S. trades more than the others, so it benefits more from not having pirates roaming around the waters.
    4
  773. Certified first!
    4
  774. Yep, that makes my head hurt.
    4
  775. They are in order, so you can just let the playlist run.
    4
  776. Damn you got me…
    3
  777. YouTube failed to convert them for a few minutes. They are working now.
    3
  778. Ah, okay. The second part of my comment was addressing that point, but let me provide a clearer articulation. Claim: For any row or column, there can only be at most one winning square. Proof: For proof by contradiction, suppose there is more than one. Of those, consider the square furthest away from the top right corner and the next winning square within row or column. Call the first one X and the second one Y. Because the piece can move any length within a row or a column, it can go from X to Y. Because Y is a winning square, the player who landed on it wins the game. But X is also a winning square, so whoever landed on it also wins the game. However, if a player lands on X, their opponent can move it to Y. Thus, both of those players must win, a contradiction.
    3
  779. Thank you so much! That was generous of you.
    3
  780. Sorry my friend. The video was ready to go but sometimes YouTube gets complicated!
    3
  781. Certified first!
    3
  782. +LegateRikke There isn't a clean answer. Using the payoffs from 6:18 in the video, the first mover has a greater payoff if 1 > 2 d_B (1 - d_A). I don't think there is much to see there other than that this is more likely to hold when d_A is large and d_B is small, which is exactly what you would expect. (That is, the first mover is more likely to get more when the first mover is patient and the second mover is impatient.)
    3
  783. jvgama Right. This can be a little confusing. Everyone is correct here. Discount factors range from 0 to 1, with 0 being highly impatient and 1 being highly patient. So when you "increase a discount factor" you are increasing patience, not discounting.
    3
  784. We're gonna do an entire video on that later!
    3
  785. Surprisingly not burnt out but I can at least sympathize as someone who fears that will happen
    3
  786. I humbly note your note regarding the noted.
    3
  787. Umm. Thanks!
    3
  788. There will be virtually nothing about voting and social preference aggregation. We will take states' preferences as a given and work with them on the international stage. You might be more interested in comparative politics, which is more geared toward what you are talking about.
    3
  789. Well, I made a mental note to reference a sledgehammer the next time those three come up again...
    3
  790. “Crisis bargaining theory” or “the bargaining model of war”.
    3
  791. Well, think of it this way. Suppose I get paid $1,000 every year. If we added it your way, then the value of the annuity for year 51 would be 0. It makes sense that the utility would be small---that's a LONG time away---but I would certainly rather have an extra $1,000 when I'm in my 83 years old than not. Using the geometric way, the annuity for the 51st iteration in today's terms is .98^50*1000, or roughly $364. Another way to see the problem with the suggested way is to put yourself in my shoes when I receive the 50th iteration. Should I think of the 50th iteration as infinitely more valuable than the 51st iteration? 82 year old me would be very confused why 83 year old me does not care at all about $1,000. The geometric way also solves this problem. 82 and 83 year old me internalize the same difference as 32 and 33 year old me.
    3
  792.  @RE-ec7iz  Dog Town for life.
    3
  793. I think the most likely outcome is status quo ex ante.
    3
  794. Certified first comment! (Yo.)
    3
  795. +Simona Pociute Civil wars: http://www.colorado.edu/geography/class_homepages/geog_2002_s06/laptop_s06/current%20projects/Cox_Low%20Robinson%20Book%20chapter/Cox_Low%20Book%20chapter/walter%20-%20end%20of%20civil%20wars%20IO.pdf I can't seem to find the proper citation for the more recent study on civil wars. (It's been four years since I filmed this...)
    3
  796. I'm not sure exactly what you mean, but there's no source of uncertainty in this game. Both sides know exactly what the other wants, so they both know that the other will end the game with defection, which sabotages cooperation in the earlier periods.
    3
  797. I thought about discussing one-time optalythic data rods, but that was probably too much
    3
  798. Sounds like you are thinking of provocation? https://www.youtube.com/watch?v=WRbmUifq-6U&list=PLB5965C13F4B0B2DA&index=77
    3
  799. I don't know what that is, so probably not?
    3
  800. Traveling this week and next week. There will probably only be one new video over the next ten days.
    3
  801. I took a walk after I uploaded the video and thought to myself "I'm not sure whether I said 'asteroid' or 'meteor'." Oops. At least I didn't go with meteorite...
    3
  802. Ah, the dreaded mirror match!
    3
  803. 90s era VH1. It was a good time to be alive.
    3
  804. I am more knowledgeable about the East Asian allies, and I can say with some confidence that those countries don't really follow the pollution concern. It's more like the threats were consistent until the U.S. resolved the problem. I am not too worried about Argentina and Brazil either, though I am not as substantively knowledgeable about their relationship. They had a series of nuclear agreements, and we went with the first one for the types of reasons you described. For example, we could have chosen 1991 for the creation of the ABACC. But we actually chose the Declaration of Iguaçu in 1985. (The figures are comparing before and after 1986 due to the way the data are structured.)
    3
  805. It was so hard to resist the temptation once I said "thirty-three and a third."
    3
  806. That's a good question. I had to think about it for a few minutes, but the answer is no. Here's why. The finitely repeated game is trivial. At the last stage, Albert offers Barbara 0 and Barbara accepts, just like an ultimatum game. The value of 0 travels all the way up for Barbara, meaning she ends up receiving nothing. The infinitely repeated game is more complicated, but the solution concept is the same thing we see in the Rubinstein proof. For simplicity, assume stationary strategies. Let d be the discount factor and V be Barbara's continuation value. Then in any generic period, Albert needs to offer Barbara at least dV to induce her acceptance. He won't offer any unnecessary concessions, so the optimal offer is exactly equal to dV. But that makes Barbara's continuation value equal to dV. So we have V = dV. But d < 1. So the only way this can hold is if V = 0. QED.
    3
  807. I had to look this one up. It appears that the survey was exclusively looking at non-state terrorism definitions, so I think that explains that.
    3
  808. As far as I know, there isn't much to say on that topic. My understanding is that the Geneva Conventions define what a civilian is, and there is not much disagreement there (in contrast to terrorism).
    3
  809. Unfortunately, this is the worst-performing upload from the recent past, so I'm not sure! I have a couple of ideas, but it may be a while before I try again.
    3
  810. Gustavo Cardenas There are multiple hares on the range. If both hunt hares, they will split that amount. If only one hunts hares, that individual will get all of them.
    3
  811. Most of these are made for classes I teach in the real world, so I don't pay too much attention to the views of new releases.
    3
  812. Your choices should be independent of one another. Playing rock in a previous round should make you no more or less likely to play it in the next.
    3
  813.  @bozimmerman  I'm going to do a video on that uses part of Logic of Political Survival in a couple of weeks. Just haven't gotten there yet!
    3
  814. That's because the prisoner's dilemma has a commitment problem. This one has time-inconsistency unlike PD. (To see this, reverse the moves and see what happens.)
    3
  815. I split recording over two days. Before the break was my voice from Friday. After, it was this morning.
    3
  816. I don’t know, but I am definitely turning left as soon as the light turns green!
    3
  817. The comment at 4:05 is beliefs about Russian pits and not about American ones.
    3
  818. And certified so!
    3
  819. Those are betting odds, not poll numbers.
    3
  820. Two is fine, one is no good. I will leave the backward induction for that up to you. :)
    3
  821. Fortunately, it's possible for you to not have any, give me none, and still remain captain. :)
    3
  822. I thought it was an interesting experiment, but I am waiting to see retention metrics before determining how frequently I will do similar things.
    3
  823. It’s actually very common for oil states! It doesn’t take much labor to extract oil wealth, so it is easy for it to concentrate in the hands of whoever has the property rights.
    3
  824. Definitely sill happen in the near future!
    3
  825. That is absurdly generous, thank you!
    3
  826. All of this holds if you allow for war to take on a bunch of different outcomes (I win everything, I win mostly everything, you win slightly, you win greatly, we draw, etc.) with different costs associated with those outcomes. The only thing you need to get the result is that the costs are actually costly, i.e. c > 0. And that's not a very heroic assumption, since war very obviously kills people and destroys buildings. War doesn't make anything magically appear except destruction.
    3
  827. If you look carefully, there are brackets where the .25 gets distributed like (I think) you thought.
    3
  828. And first comment!
    3
  829. Happy to help!
    3
  830. I cover risk aversion in another video. Regardless, consistent risk averse preferences do not violate the independence axiom.
    3
  831. I was guessing how long it would be when I wrote that and found out later that the natural length was longer
    3
  832. Nope, the book stops at around video number 40 or so.
    3
  833. Good catch. It looks like it should be 10 + e - e^2.
    3
  834. Thank you so much again!
    3
  835. Thanks!
    3
  836. That would depend on whether P2 lucks into the right solution. Can’t really say much beyond that.
    3
  837. Just got an email from WotC inquiring whether I was available to lead vision design...
    3
  838. Looks like I spent too much time thinking about Samoa Joe Biden that I forgot what happens when you add Kurt Angle into the mix…
    3
  839. Second, sorry!
    3
  840. May Big Boss forgive me.
    3
  841. I don't understand the question.
    3
  842. The suggestion from @samter sounds right!
    3
  843. It’s hard to define a metric to answer that question. All of these types of games are inherently unbalanced because either the first player can guarantee a win or the second player can. At the very least, adding that rule would require rethinking the problem—-though, I think playing in the middle of an odd board and then strategy stealing from thereafter would still win for that rule set.
    3
  844. I really want to add "Living" to your username.
    3
  845. I did one a while ago with the Series 1 finale. Search "game theory sherlock" to find it.
    3
  846. That remains an open question. The paper I linked to in the description did not have voting data, so they couldn't make such judgments.
    3
  847. A p = 1 (or a p = 0) value would give you the best (or the worst) choice with certainty. It can't be that you are indifferent between your best (worst) choice with certainty and your middle outcome with certainty.
    3
  848. +jvgama Yeah, that would work. (I think...I don't know much about engines. Haha.)
    3
  849. Yay! Thank you!
    3
  850. I only have a few more left planned, and no book!
    3
  851. It’s just PowerPoint!
    3
  852. If you confess, you get eight months if the other guy confesses as well. You get no time in jail if he keeps quiet.
    3
  853. I don't understand your calculations. Let p be the probability the other guy keeps quiet. (In your example, p = .5) Then my expected time in jail for not confessing is (p)(1) + (1-p)(12) = 12-11p. My expected time in jail for confessing is (p)(0) + (1-p)(8) = 8-8p. Note that 12-11p > 8-8p simplifies to 4 > 3p. This has to be true, since p at most can equal 1. Therefore, regardless of the other player's strategy, not confessing yields you more jail time. So you should confess. Clear?
    3
  854. Good luck!
    3
  855. The book I always recommend to people is The Evolution of Cooperation by Robert Axelrod.
    3
  856. This is partially why third-party exchanges and seller/buyer reputation systems developed.
    3
  857. “The gang goes to Ukraine” has a good ring to it.
    3
  858. Discovery disaster (n): William Spaniel unable to remember the difference between Columbia and Discovery. First observed on 3 January 2023.
    3
  859. My next video is a long-form analysis of Putin’s miscalculation. My next long-form video after that will be the Battle of Kyiv. There may be some shorter videos in between, though.
    3
  860. Gotta represent!
    3
  861. I have an example like that already written down! "Sabotage Drafting: A Game Theory Puzzle" Might be a bit before I try any of these again, though. Viewership is down for this one. Not sure if it's because it's gridiron football or what.
    3
  862. Hi General 12th!
    3
  863. Point of clarity at 3:50 because my phrasing was ambiguous: Luhansk is only missing Sievierdonetsk at this point, which is why it has been in the news so much recently. The Russian gains in Donetsk have not been as extreme, with the concentration of those changes coming in the south to form a land bridge to Crimea. This is enough to give Russia control the majority of the oblast. Combined, this gives Russia immense coverage of the Donbas.
    3
  864. lol well that was a change of pace
    3
  865. Thank you!
    3
  866. heavengaze Psychology is great, but you are still left trying to explain why peace is FAR more prevalent than war. As far as I know, there is no explanation for this that does not eventually appeal back to bargaining and the inefficiency of war.
    3
  867. I do it because it is helpful for non-native speakers. I breathe all over the microphone if you aren’t sure if it’s real.
    3
  868. Can you describe that in a more detailed way?
    3
  869. Hope it goes well for you.
    3
  870. The subtitles are manually written, so it was my own conscious choice.
    3
  871. Second!
    3
  872. Short answer: Even if Russia were to just back off, I still think the message has been sent. Georgia was moving toward NATO expansion in 2008, Russia intervened in the conflicts in Abkhazia and South Ossetia in large part because of that, and Georgia-in-NATO has been dead in the water since then. Few in NATO are going to be excited to begin a path forward for Ukraine to join if it is just going to put us right back where we are now.
    3
  873. Then you have a civil war AND an interstate war. It's very common for civil wars to have some sort of international crossover.
    3
  874. Thanks, I’ve been working hard on improving editing!
    3
  875. Fifth!
    3
  876. Can't really help you for three reasons: 1) I'm not really sure what you mean by math applications. Technically, every field that uses game theory is turning their area of study into math. So everything kinda counts. 2) My focus is on war bargaining. As a result, I know a lot about war. So I don't know very much about auction theory, etc. 3) Virtually all game theory texts are horrendous. That's one of the reasons I'm doing these videos. Can you be a little more specific on what you need?
    3
  877. It’s actually a technical term that takes years to understand the true meaning!
    3
  878. Thank you!
    3
  879. The economic peace is a statistical trend, not a law. A single case does not falsify anything. Moreover, UK/German trade in 1913 amounted to $13 billion in 2012 dollars. US/China trade was $535 billion last year.
    3
  880. And it will! ...in August 2018.
    3
  881. Third, sorry!
    3
  882. You just made me laugh out loud in a quiet public area. Well done!
    3
  883. The key result from expected utility flips that thinking. We aren't trying to say that people have real numbers as preferences. Rather, as long as someone's preferences meet the axioms from this unit, then we can use preferences to represent numbers. So its preferences that cause numbers, not numbers that cause preferences.
    3
  884. +Kobe Bryant from the Lakers Hi Kobe, it's great to see that you have apparently studied some heavy mathematics while recuperating from your injuries. The preference function does not need to be a bijection. I have mentioned a couple of times that indifference between two outcomes is perfectly fine. Indifference assigns the same utility, which thereby prevents a bijection. In fact, we will see later that expected utility functions CANNOT be bijective. Even if you have an individual who is not indifferent between any two outcomes, he must be indifferent for particular lotteries (i.e., random assignments) over outcomes. So, to summarize, it seems you are "missing the point here" insofar as we only need to map preferences to utilities and not vice versa. Thus, we don't need to worry about whether a function is bijective.
    3
  885. The payoffs are correct. Mutual cooperation (3, 3) is worth more than mutual defection (1, 1). These don't represent years in jail. You want to maximize your payoff, not minimize it.
    3
  886. The complete playlist (including the unpublished content!) is here: https://www.youtube.com/playlist?list=PLKI1h_nAkaQrvKPtuPMXkU4yXCDSp_NHh
    3
  887. This was part of the strategy in Berlin during the Cold War: there weren’t enough troops there to do anything to defend the city, but there were enough troops to cause enough problems that the US would definitely retaliate in some manner.
    3
  888. Thanks for the kind words! I don't worry about the dislikes too much. These are essentially videos about politics, and that will always cause a few people to get mad.
    3
  889. I might do a short one on this topic in the near future!
    3
  890. Certified first!
    3
  891. Third!
    3
  892. Second!
    3
  893. Definitely want to start at the top of the playlist!
    3
  894. Game Theory 101 MOOC (#37): Mixing among Three Strategies The math gets complicated very quickly outside of 2x2 games. I have a couple more examples and tricks in the textbook, but it's not easy.
    3
  895. I have a small brain.
    3
  896. It's the same process either way, so whatever works for you. I think doing Ts before Fs is more common, though.
    3
  897. Second =(
    3
  898. Imagine that the players have the same marginal costs so that c_1 = c_2 = c, and then simpify.
    3
  899. +treeman258 It's been a while since I have read that literature, but I am pretty sure that tit-for-tat does very well in those cases.
    3
  900. The term itself is not nuclear-specific. Here's the general idea: https://en.wikipedia.org/wiki/Pork_barrel
    3
  901. Actually, I mix. Sometimes I have the right solution. Other times, the thumbnail deliberately shows something that seems like it should be the right solution, but isn't. Don't trust me or my thumbnails!
    3
  902. That would have been a good thing to add to this. Opportunity lost!
    3
  903. If you are the one who I exchanged comments with on the last video, then yeah, I 100% was not going to do this until that conversation.
    3
  904. My programmers won't let me know whether I am...
    3
  905. Second!
    3
  906. It's some algebraic manipulation from the line above.
    3
  907. Is this a reference to something I said? :confused:
    3
  908. Ah. The benefits of subscribing.
    3
  909. How about NEATO, the North European and American Treaty Organization?
    3
  910. Fifth! =/
    3
  911. My general rule is "include more complicated things when it matters for what you are discussing." You are correct that a delay would reduce the value of the alternative. But it will still be some value (like d*y), so the same general idea still applies. Likewise, you could fully model the negotiations between Barbara and the third party. But again, that would still give Barbara some value for rejecting (now endogenously determined through those new negotiations), and the same general idea would still apply. TL;DR: Keep it simple whenever you can.
    3
  912. Mmm
    3
  913. It's the opposite actually. If they were to repeat this game any finite number of times, the only equilibrium is to play the strategies described in the video. (It's also the case that in any finitely repeated game, playing the equilibrium of the one-shot game in every period is also an equilibrium.) In infinitely repeated games, it's possible that new equilibria can arise. See as further discussion and examples: https://www.youtube.com/watch?v=Vy5reCmEfBg&list=PLKI1h_nAkaQoDzI4xDIXzx6U2ergFmedo&index=20 https://www.youtube.com/watch?v=8jBouAQt9EY&list=PLKI1h_nAkaQoDzI4xDIXzx6U2ergFmedo&index=60
    3
  914. Glad you are enjoying them!
    3
  915. Second :(
    3
  916. Good news, the next NATO summit is just three weeks away.
    3
  917. First person to spot him, congrats!
    3
  918. Yeah, that's definitely the case with Iran/Iraq/North Korea/Libya, but I am not sure how much to read into it.
    3
  919. I did some rough calculations on this, and it looks like you would need the right improvement to be at least ~2.25% or greater in improvement to be better than the 2% gain on the left side. I have a problem that does something like this with football free agents. It should be scheduled for the end of August.
    3
  920. Hadn't seen that paper before, thanks for sharing!
    3
  921. Let's assume that the consumer randomizes evenly among firms that she is indifferent over. Then one of the low price guarantee firms could profitably deviate to a slightly smaller amount. By doing so, it and the other low price guarantee firm each receive half of the business rather than a third. So higher prices are unsustainable without the other firm offering the guarantee.
    3
  922. Well, I do think that it would be good if more people were aware of the second-order consequences of low price guarantees!
    3
  923. You're welcome! I would amend that to say "there are conditions where low price guarantees are anticompetitive." Models are good for telling us what is true for a given set of assumptions. The set of assumptions described here do not preclude other assumptions under which low price guarantees are good for consumers.
    3
  924. I have a few more ideas for variations on RPS, so I will try my best!
    3
  925. Not for much, though. Probably not doing anything else until I have to make some corrections to my international relations lectures. Will probably do a completely new section on terrorism.
    3
  926. Ding ding.
    3
  927. Fifth ain't bad.
    3
  928. There is some work on that. An example: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.891.1974&rep=rep1&type=pdf
    3
  929. I would describe this more as a combinatorial game theory problem than a graph theory problem, though I suspect if one were familiar with graph theory (which I am not, other than in the most basic sense), they would have more insight into it than someone who does not.
    3
  930. Fourth, sorry.
    3
  931. Sorry I ruined your Sunday!
    3
  932. Oops, that went right over my head. Love that series, though.
    3
  933. Thanks for the kind words!
    3
  934. Self-fulfilling prophecies don't have to "work" for all players. You just need to have each individual's action be the best they can do for themselves given what everyone else is doing in the self-fulfilling prophecy. Battle of the sexes is a good example of where a self-fulfilling prophecy can be bad (but still better than the alternative) for someone: https://www.youtube.com/watch?v=2BdBWmL8tJc
    3
  935. Yeah at first I thought it would be something like that, but then I noticed it starts getting messy. It’s like the top rows have a spillover effect that the lower rows take a while to fully recover from.
    3
  936. This is true up until the second row. That made me start wondering if this would be the case if you could take up to three (or up to four, or up to whatever). It looks like that still happens in the long term, but it takes A LOT longer when the limit is more than two. For example, with three, the pattern doesn’t start until row eight.
    3
  937. That's the right idea, with a bunch of caveats. For example, player 1 doesn't win for a pyramid of any height. (For proof, take a look at what happens in the video if you ignore the bottom row.) But it is true that if P1 should win by going first that a single mistake will give P2 the ability to control the win from then on. (Of course, another mistake by P2 allows P1 to control the rest of the game.)
    3
  938. A long time ago. =)
    3
  939. There is a very complicated way the General Assembly can do this by shifting recognition of Russia to some entity that isn't Putin's government, but there is basically no chance it will happen here. It did happen with ROC/PRC, though, which is how the UNSC got where it is today: https://youtu.be/3a_-NojmIPA?t=513
    3
  940. That's often why such resolutions are put up for a vote even though their supporters know they are destined to fail. And there have been *a lot*. https://en.wikipedia.org/wiki/List_of_vetoed_United_Nations_Security_Council_resolutions
    3
  941. Ugh. Yes.
    3
  942. First!
    3
  943. The books are all Kindle-exclusive. Just search Amazon for Game Theory 101 and you will find them. The full textbook is $3.99.
    3
  944. Here, we have assumed that the firms have identical discount factors. Relaxing this is simple. The 9/17 cutpoint is calculated the same way for each firm, and you need each firm to be willing to follow the cartel's rules for the cartel to work. Thus, the cartel can only work if delta_1 > 9/17 AND delta_2 > 9/17.
    3
  945. I said that profit is relatively low, not zero. That's an importance distinction! (Profits are indeed zero under a symmetric Bertrand game, though..)
    3
  946. And a fellow Rochester student at that!
    3
  947. If you google "game theory calculator", there are a lot of options for solving matrices. There isn't something you where you could specifically design trolley problems like these and have them calculated without you having to manually convert the payoffs to a matrix.
    3
  948. The nuclear book? Happy to hear it!
    3
  949. You found him!
    3
  950. No, Israel in 1973. There are differences, of course. That is the plan for the next video.
    3
  951. That is correct, though you have to apply double negation to get there.
    3
  952. Left is player 2's strategy. Player 1 cannot remove a strategy he cannot choose.
    3
  953. @Daggroth Hmm, it seems that there is some miscommunication here. When you are finding strictly dominated strategies, you can only look at the payoffs of the player whose strategy you are trying to eliminate. But once a strategy has been eliminated, you can ignore that part of the payoff matrix for BOTH players. That is what makes IESDS such a useful tool.
    3
  954. @thecapone45 Yes, and this is one of my research interests. There exist a few academic journals for game studies, but they currently lack this kind of structure.
    3
  955. Peter Martinez Yeah, this series has been really slow going for me.
    3
  956. I think you were the first!
    3
  957. It was actually Milley's seat I covered up! =D
    3
  958. Russia has tanks that are better adapted to the terrain. But as we have seen in the three months since this video was published, they aren't perfect solutions.
    3
  959. Entirely different, yes.
    3
  960. Then you'd have to change the payoffs entirely.
    3
  961. I think that's either covered with Afghanistan (if U.S/other NATO countries continue to provide aid, like is currently happening) or with World War III (if they militarily intervene). Maybe you had a third idea in mind?
    3
  962. I understand your point, but Bach or Stravinsky is not anywhere close to the "common name" for that type of payoff structure. There are about 500,000 google results for "'battle of the sexes' game theory" but only about 5000 for "'Bach or Stravinsky' game theory". Of those 5000, 4000 contain the word "battle" anyway. There is a good argument to be made that we are inferior equilibrium of a coordination game, which I suppose is a lesson all of its own.
    3
  963. I suppose that's what I get for creating a down arrow, using the Russian flag as its background, and THEN flipping it around.
    3
  964. Your example captures the central logic: the pace gets faster with each iteration. It just works more aggressively than the ratio of that particular magic jar. For example, getting to 20% enrichment is 90% of the work: https://armscontrolcenter.org/uranium-enrichment-for-peace-or-for-weapons/#:~:text=The%20simple%20answer%20is%20that%20enriching%20uranium%20to,ready%20to%20weaponize%20in%20a%20relatively%20short%20time.
    3
  965. The video is correct. The goal of enrichment is to "find" U-235 atoms. In a natural state, this is difficult because it makes up less than 1% of what comes out of the ground. As you start discarding the junk isotopes, it becomes increasingly easy to find what you are looking for. As a result, the halfway mark is about 5%. It is counterintuitive because of the size of the numbers, but the goal is not perfect separation. It is just to find what you are looking for.
    3
  966. Player 2 would have three types (uninformed, knows it is heads, and knows it is tails). There would be a cutoff on the probability that P2 is uninformed that would allow P1 to choose to play despite the fact that he will lose to the informed types.
    3
  967. Tomorrow!
    3
  968. Next week. Iran does not have nuclear weapons, so they aren't on the list here.
    3
  969. You are right, thanks for letting me know!
    3
  970. +onfire4000 No. PBE is a part of the planned update, but it will be at the very end of the new cycle. It is months away.
    3
  971. The first official #whereszelensky champion!
    3
  972. It's no one in particular. The issue is as pervasive as it is frustrating.
    3
  973. darkj (If I am understanding your question correctly...) Yeah, this is tricky. As a matter of convenience, you can always multiply both sides of an inequality (i.e., utility comparison) by a positive number and maintain the proper relationship. So if we were comparing period n to period n + 1, both of those should be discounted a whole bunch of times. But if we are comparing n to n + 1, we only need to care care that n + 1 needs to be discounted once more than n. So we can multiply away the remaining discount factors and clean up the comparison. This is done a lot in repeated games. It takes some getting used to but it makes life a hell of a lot simpler.
    3
  974. Eventually! But way, way later in the course.
    3
  975. I'm going to try uploading duopoly stuff when I can, but it's definitely a secondary priority. The nukes class is what I am teaching IRL right now, so I have weekly deadlines that I have to meet for it.
    3
  976. That's three lectures ahead.
    3
  977. The p value covers amount of territory received (won/lost) through war. The costs are just money, lives, destroyed builds, etc.
    3
  978. Next week. =)
    3
  979. Glad to hear it. Congratulations!
    3
  980. In fact, there is a theorem that says that such a solution won't work for the reasons you described! https://youtu.be/c8HD_ipLSb8
    3
  981. Crazy, right?
    3
  982. I had a hard time finding the exact process they used. The thing with adverse selection, though, is that even a little bit of it can cause a large problem. Even if you had an inspector check on the inside for things like plumbing, an algorithm could still struggle with things like “is painted an ugly gold color” and we are back to the central problem.
    3
  983. Calculating the general case for n players is easy to do with symmetric marginal costs. Going back to the last video, the first order condition for Firm 1 was a - 2q_1 - q_2 - c = 0. So rather than think of just q_2, imagine instead that it was q_2 + q_3 + ... Looking for a symmetric equilibrium where each produces the same q and substituting with n firms that makes the first order condition a - 2q - (n - 1)q - c = 0, or q = (a - c)/(n + 1). So, with two firms, you would have (a - c)/3, like in this video. The profits are easy to calculate from there. Maybe I will do a video on this before going to Stackelberg.
    3
  984. Right. The next lecture is going to be about why there is a significant problem with trying to implement that as a solution.
    3
  985. I prefer King Cavalier for my son and Brittany for my daughter.
    3
  986. No, everything just streams. Sorry.
    3
  987. Yes! As of 2015.
    3
  988. Nope, that’s my real voice.
    3
  989. Thank you!
    3
  990. Kind of. I have an unlisted playlist on war that contains a lecture on cheap talk: https://www.youtube.com/watch?v=N4OIgoPXjAQ&list=PLKI1h_nAkaQrvKPtuPMXkU4yXCDSp_NHh&index=26&t=0s Doing a more general version is in the long-run plans for the main game theory playlist.
    3
  991. You can do it like that. In fact, you can change the payoffs by adding an arbitrary constant to all of one player's payoffs, and nothing changes. (A nice exercise would be to replicate the results from this video with new utilities like that.) Actually, when I wrote the first draft of the book, I had the payoffs closer to what you are suggesting before opting for these instead.
    3
  992. Yep, plan is to do that after Stackelberg.
    3
  993. At least insofar as the comments go, I think so!
    3
  994. Certified first!
    3
  995. It is 100% my own voice.
    3
  996. Thank you!
    3
  997. Meliora!
    3
  998. Me opening my lips?
    3
  999. I still am. I'm in a PhD program.
    3
  1000. +sinecurve9999 I think you are right.
    3
  1001. Thank you so much! That was very generous.
    3
  1002. It means that all players are doing the best they can given what the others are doing.
    3
  1003. Well, the game master doesn't actually play any game. He just takes the information that the players tell him and hands out payoffs based on that information. What guarantees the existence of incentive-compatible direct mechanisms is the fact that the game master can use an allocation rule that duplicates the outcome of the game had they just played it for themselves. So, outcome wise, there is no difference.
    3
  1004. Short of taking an actual class on the subject, this is the most thorough summary I have: https://www.youtube.com/watch?v=pBwT-5z9R5A This is the class: https://www.youtube.com/playlist?list=PLKI1h_nAkaQrvKPtuPMXkU4yXCDSp_NHh
    3
  1005. Thank you!
    3
  1006.  @swapnilkamble111  GT101: https://amzn.to/2Uw3iN0 GT Evolving: https://amzn.to/2QIILWt
    3
  1007. That's amazing! Thank you for the update, and congratulations!
    3
  1008. I sure hope so---even if no (hopefully) has ever actually paid that much for it. (MSRP is half that.)
    3
  1009. Yep! And that's a general property of mixed strategies: you need to choose a mixture that induces indifference from your opponent. Thus, small changes to your payoffs do not change your strategy, only changes to your opponent's. (Large changes to your payoffs can give you a dominant strategy, hence the "small" caveat.)
    3
  1010. In what way?
    3
  1011. It's limited to things you can actually put into a matrix form. Something like Hotelling's game wouldn't work with this because the strategies any given type can choose are infinitely many.
    3
  1012. +mjja61 Probably months, and definitely not before this academic school year finishes---I have ~9 more lectures of BNE to do, and I also have a cross-country move to plan.
    3
  1013. Wow, thanks!
    3
  1014. Something like that would better sort out whether people are irrational in answering the question or simply responding to what they observe. I think a more precise question would be to ask "are you a better than average driver?" and then ask "how confident are you that you are better than average?" The one issue here is that there is some subtlety in that second question, and I wouldn't be fully confident that someone answering it would understand what the survey is intending.
    3
  1015. Whoops, thank you!
    3
  1016. Go to my website (william spaniel followed by a period and then com), click papers, find "Does Increasing the Costs...", and check footnote 1. (Sorry, YouTube won't let me post a direct link.)
    3
  1017. Your avatar tricks me every time. =(
    3
  1018. Aren't we all?
    3
  1019. Oh my bad
    3
  1020. Guilty as charged 😅
    3
  1021. That's very kind. I should get the physical copies in the mail on Tuesday, and if everything is fine then it should be 24 hours after that. But I might find printing problems! Then it might take longer. But I will definitely note when they are available in the "normal" video that I will release after it.
    3
  1022. Not yet but we’ll see…
    3
  1023. @AK1MB0SL1C3 Nash equilibrium only looks at deviations from a single player. It is true that if both players simultaneously deviate to stag then both players make a profitable deviation, but that is a coalition of deviations, not an individual deviation. I wouldn't use "cartel" to describe the situation, as the word has a negative connotation. Moving from (hare, hare) to (stag, stag) is not predatory. In fact, it benefits everyone. Hope that helps.
    3
  1024. Since we are dealing with economic production, a straightforward interpretation of the discount factor is interest rate. That is something that is readily identifiable empirically. There may be differences in discount factors for other reasons, though, and we will cover that in Rubinstein bargaining. It may then be difficult for Albert to exactly identify Barbara's discount rate. We will  talk about that issue when we get to incomplete information, which will be a while.
    3
  1025. This is a simultaneous move game, so P1 can't respond to any observed moves of P2. What you were saying would be the case if this were a sequential game and we were looking for PBE.
    3
  1026. Had to finish Game Theory 101 first.
    3
  1027.  @PunmasterSTP  Probably. It still lags to some degree today, and my comment here was from 9 years ago. I can only imagine it was worse back then.
    3
  1028. Your endless consumption of these inspires me to make more! It's not going to be long until you have gone through everything.
    3
  1029. Thanks!
    3
  1030. No idea about logic. There are a couple of game theory series on YouTube that go into a bit more depth: https://www.youtube.com/user/gametheoryonline https://www.youtube.com/watch?v=nM3rTU927io&list=PL6EF60E1027E1A10B
    3
  1031. I'm surprised it took more than 24 hours for someone to point out this fatal flaw in the puzzle.
    3
  1032. Bayesianists vs. frequentists? I'd have to change the utilities so that they actively value putting the cart in front of the other. =O
    3
  1033. I consider myself to be a Theodor Blueger Stan.
    3
  1034. Yep, as long as you are adjusting the viewpoint along with the draft order, it works!
    3
  1035. +Ibrahim Alallaqi Are you thinking of a destructive dilemma? https://www.youtube.com/watch?v=x8Y-DvqZocA
    3
  1036. Exactly what a cheater would say...
    3
  1037. Yeah, I also thought that the implication was neat the first time I read about the result.
    3
  1038. I pulled the information on foreign deployments from here: https://doi.org/10.1177/0022002713509055
    3
  1039. Thanks Obama
    3
  1040. Thanks as always!
    3
  1041. Thank you!
    3
  1042. Incredibly generous, thank you again!
    3
  1043. I hope so too! Thanks!
    3
  1044. Thank you so much! Very generous.
    3
  1045. beep boop
    3
  1046. It’s a book about how academics think about war, except completely focused on Ukraine. Up to you to decide whether it is biased from there…
    3
  1047. Quicken Loans bought an insurance policy from Buffett for the contest. Thus, Quicken would not have paid anything had someone won the contest. http://www.cnbc.com/id/101494540
    3
  1048. I can't speak to the countries you are referring to directly, but something like this was an issue about six years ago. There was speculation that Turkmenistan might offer use of its bases. But regardless of the country and cheap-talk public declarations, the real question Iran faces is whether those countries would actually allow Israel to do it when push comes to shove.
    3
  1049. This is the playlist: https://youtube.com/playlist?list=PLKI1h_nAkaQppKwAw3BuwMwe0IvmZ5oei
    3
  1050. Zero if you are going for presidential line of succession. Outside of that, the lowest I can get to elect a president is 27. No citizens vote in the election. All 538 electoral college votes go to different people. There is a contingent election in the House of Representatives, which must choose one of those 538 people. The states vote in blocs and require a majority, so 26 votes are cast for a single person. That person becomes the president.
    3
  1051. No problem. Check out the PDF of chapter 2 of the book on my website (or the whole book on Amazon). You will see that the math isn't difficult. The logic is really demanding, yes, but the math is mostly basic algebra and sometimes a tiny bit of calculus.
    3
  1052. Probably the most important thing! Watch the next video...the geometric model is much easier to interpret. It also gives you something visual to stick in your mind.
    3
  1053. Right, this is a little tricky. My "costs" for war appear smaller to defend Minnesota than they would be to defend Mexico because I am willing to sacrifice more to protect Minnesota. So, despite how I might be losing 10,000 soldiers, I internalize the costs as being less costly for Minnesota than Mexico. TL;DR: Costs are a function of the physical costs and how much I care about the issues at stake. (Maybe I misspoke in the video. If this is clearer than what was in the video, go with it.)
    3
  1054. It probably won't (depending on where you go). But that's NOT a good thing. This is where the field is today. If you go somewhere that doesn't give you any introduction to this, you are getting a masters in political science from 20 years ago.
    3
  1055. Not today!
    3
  1056. I don’t have anything directly planned, though I could see Germany coming up in regard to the winter/gas and maybe use Croatia’s independence as a historical example for something else entirely.
    3
  1057. Yep, the bound could be slightly lower.
    3
  1058. Yep, that's right! And like you noted, the issue with very low tolls is that the patient drivers begin to "pollute" the speed of the toll road despite not making the patient drivers any better off (due to the cost of the toll).
    3
  1059. Uh oh, you found a new playlist!
    3
  1060. That would certainly be the case if a toll was already set at, say, $5. A higher toll does not Pareto dominate that amount precisely for the reason you described.
    3
  1061. Welcome to the channel. I promise that most of these aren't derivative-fests. :)
    3
  1062. If both choose without knowledge of the other, it becomes a standard Tullock contest. I explain that here: https://youtu.be/jIfk2Pplxz8 And, yeah, bribing your opponent would be better for everyone. These types of contest models are standard in the war literature, and I have written a paper about that sort of bribery (the difference here being one-sided endogenous effort but uncertainty over one of the party's valuations): https://williamspaniel.com/papers/bargaining-over-costly-signals/
    3
  1063. You're welcome! There will be a puzzle based on a model from that book the week it comes out, so it will be easy to remember.
    3
  1064. It looks like August 31. I don't have any additional information beyond what is publicly available. But everything is done with the manuscript, cover, pagination, and so forth, so I'd be surprised if Cambridge makes any changes.
    3
  1065. There are a ton of versions of this problem out there, but I am not familiar with a deeper connection to anything beyond dynamic programming.
    3
  1066. Not yet produced. Will probably pick back up on it during the summer.
    3
  1067. Thank you! Please leave a review over on Amazon when you are done. It really helps out.
    3
  1068. And first comment, period!
    3
  1069. You mean from like a week ago? Just depends where the natural break is in the material.
    3
  1070. stormscape10x What could change things is if the demon thinks you are dumb. Then green might start looking reasonable if he’s expecting blue. I have something similar to this in mind for way down the road!
    3
  1071. stormscape10x The demon is already strategizing against you knowing that you are also thinking strategically. You’ll notice that if you select red, he can’t do better than play orange.
    3
  1072. 2021 Me: This is a video about liquidity in banking, so that's what the title should be. 2022 Me: This video is genuinely interesting, but people don't think liquidity in banking is very interesting. So let's definitely not title it that, people will still watch and be happy, and everyone will be better off as a result.
    3
  1073. Wow, that's amazing! That would have been perfect to mention in the video.
    3
  1074. That is (kind of) what happens in practice. The big problem with all of this is credibly committing to remove sanctions at the end of the war. In the current situation, I have no doubt that some of them will terminate, especially as it relates to the energy sector. But I can't imagine there is going to be political will within the west to return things to "normal" completely.
    3
  1075. It has some desirable properties, but the math on it is more complicated than what I want for an intro class. It's also not subgame perfect, which is a legitimate modeling complaint.
    3
  1076. Yep, incomplete information is going to be the central topic coming up in a few videos, and it's reasonable to think that black markets introduce that type of uncertainty. It's still worth caveating that under those conditions it is not the black market itself that is causing the problem but rather the uncertainty surrounding it.
    3
  1077. Right, the idea here is that the dog would only be able to sniff around, and this would not require a complete dissection of my vehicle.
    3
  1078. My favorite part is the people who still think I am AI anyway.
    3
  1079. Depending on how effective the nuclear weapons are, you might need both sides to (slowly) disarm.
    3
  1080. Fair enough. International relations is more of a mine field than game theory.
    3
  1081. One country ultimately wins or loses--they just don't know which one will ahead of time. The speculation is that 60% of the time, one will win completely and take everything; 40% of the time, the other will. Thus, to find the expected payoff for war, you need to multiply the probability winning by 1 (the value the winner receives) and add it to the product of the probability of losing and 0 (the value the loser receives).
    3
  1082. War is common enough that it is easy to rattle off a whole bunch of them off the top of one's head, especially because they are salient when they occur. But if you take any two random countries in any given year, the probability that they are at war with each other is very close to 0. It's just that there are a ton of pairs of countries and a ton of years, and so you can accumulate a bunch over time. Even the United States, the country that has fought the most wars in recent memory, still isn't fighting the vast majority of countries in any given year. Another way to think about it is that the probability that the U.S. is fighting a particular country in any given year is not the same as the probability that the U.S. is involved given a particular war is being fought.
    3
  1083. +ngyx57 Well, you want to show that player 1 shouldn't play middle. You wouldn't want to compare middle to itself, right? So, intuitively, it makes sense to assign 0 probability to middle. A fun exercise you might want to try on your own is to compare player 1's expected utility for playing middle versus mixing between up with probability q/2, down with probability q/2, and middle with probability (1 - q). Okay, it won't actually be fun, but it might help with your understanding.
    3
  1084. This is a good starting point because it cites a bunch of the relevant papers: https://www.annualreviews.org/doi/abs/10.1146/annurev-polisci-051215-022729
    3
  1085. Further in the series, there is a unit on the repeated prisoner’s dilemma. Although I don’t frame it like this (both regarding politics and like a stag hunt), that’s basically what happens in there. And it’s also similar to how political scientists model those scenarios.
    3
  1086. Page proofs for the physical copies came today, and I approved them. It could be available as early as tomorrow, definitely by the beginning of next week!
    3
  1087. In a fantastic coincidence, I filmed that video today!
    3
  1088. That’s be fitting for a video on noisy signals. 🙂
    3
  1089. Yeah, one big difference between this video and how I do it in person is that there aren't labels for each of the boxes. The players just put an X on the one they choose. The very introduction of A1 as being salient because it is smallest makes me unsure whether C3 is going to win or not. At the very least, I suspect it is going to cause more problems than it would in person.
    3
  1090. Step 1: Get tenure...
    3
  1091. There's a simple explanation to answer your question: Nash equilibrium only checks for unilateral deviations. What you described is a simultaneous deviation from two players. (One reason why allowing for such deviations is problematic: they would also eliminate the mutual defection outcome of a prisoner's dilemma.)
    3
  1092. The next video in the series calculates the payoffs: https://www.youtube.com/watch?v=4lEl4vDkML8&t=3s
    3
  1093. Thanks! I hope it catches on. I have a lot of fun ideas I haven’t produced yet.
    3
  1094. Fair enough. Because I can’t change it at this point: the first bit is the default probability of winning without any extra troops, and each thing multiplying the portion of troops you send represents the marginal value of that aid.
    3
  1095. That would be an issue "indivisibility" that makes bargaining impossible by assuming that bargaining is impossible. (If that sounds like a dissatisfying explanation, it is.) I have a lecture about that here: International Relations 101: Issue Indivisibility
    3
  1096. Thanks!
    3
  1097. Sorry, I'm actually teaching civil war IRL, so I have to prioritize that. I will finish these eventually.
    3
  1098. I wrote a blog post about Kindle Unlimited. It's hard to make a judgment on the program until more time has passed, but a lot of the knee-jerk reactions some authors had against it were unwarranted. http://williamspaniel.com/2014/07/18/kindle-unlimited-and-the-economics-of-bundling/ That said, you are right that individual authors do not have much bargaining power. But the system Kindle Direct Publishing has implemented is substantially better for authors (revenue sharing wise) than what existed even ten years ago.
    3
  1099. Preventive.
    3
  1100. !
    3
  1101. For the purposes of the puzzle, both would get the same amount because it’s the same person. I’m not sure what would happen if the outcomes were independent. My initial inclination would be that it shouldn’t matter, but I can’t immediately prove it in my head. And weird things can happen when things aren’t obviously provable!
    3
  1102. Yep, you are right. I noticed a mistake in the proof as I filmed the first time. In fixing it, I might have screwed up the numbering.
    3
  1103. Right. Equilibrium requires common knowledge of strategies---meaning that players can anticipate what others are doing even if they cannot observe them---and that the actors don't want to change their strategy given that expectation.
    3
  1104. And I will not abandon the enterprise of occasionally responding to comments for further engagement purposes.
    3
  1105. Certified first!
    2
  1106. Right. We want to know when war is avoidable, i.e. when both states would be willing to bargain. So we started by assuming B would want to bargain and checked when A would want to bargain as well. Then we verified that B would actually want to bargain under those same conditions that A would want to bargain. Put differently, we showed y was true by assuming x was true. Then we showed that x is true when y is true.
    2
  1107. You should think of the good valued at 1 includes all possible side payments. (This was implicitly not the case in the issue indivisibility lecture. I didn't make it explicit because it adds more complication to the model without any additional benefits...unless someone makes the connection that you did.) That being the case, no credible peaceful settlements exist.
    2
  1108. Thank you!
    2
  1109. XD Thanks for letting me know!
    2
  1110. Second!
    2
  1111. Hmm. How about a taco? Yes. I will get a taco. Thank you!
    2
  1112. Just Putin and Zelensky. It’s hard to do extra things when I don’t have time to let the project sit idle for a few days.
    2
  1113. Fifth!
    2
  1114. That's a function of the rook-style move that the amazon piece can do. You will notice that such a pattern exists in the Rook's Romp and Queen's Quest video for the same reason. Moreover, there can only be one such square: as soon as a such a square exists for any rank or file, all others cannot be a winning square because a person could instead move to that original square.
    2
  1115. Bingo! I'm enjoying the comments about how the saying could not possibly be millions of years old because the English language had not yet been invented.
    2
  1116. First indeed!
    2
  1117. Well… A new one would have come out this week if it weren’t for the Gaza crisis. 😮
    2
  1118. By subscribing. :)
    2
  1119. Yes, it was an interesting episode!
    2
  1120. It'd be a really boring 2x2 game with 0, 0 as the payoff for all cells. (0 is the expected gain when neither player can condition their choice on the card they are holding, as there is a the chance opposing card will be greater is equal to the chance that it will be smaller.)
    2
  1121. Nah I like the Stillers
    2
  1122. +Ahmad Jabri The definition of V_B is the (non-discounted) amount that B receives if she rejects an offer. We don't know what this is at the start, but we know that A will offer d_B*V_B in odd periods and B will accept that offer. This allows us to find out A's continuation value for rejecting in even periods: V_A = 1 - d_B*_V_B. We still don't know what V_B is, but we do know that B will offer d_A*V_A in even periods, and A will accept. But this means that we know another way to write out B's continuation value. This is because if B rejects an offer in an odd period, it will offer d_A*V_A in the even period and induce A to accept, yielding 1 - d_A*V_A. So that means that V_B = 1 - d_A*V_A = 1 - d_A*(1 - d_B*_V_B). Yes, this is an exercise of logical gymnastics. It took me a few days between first learning this and then accepting that it was you could actually use that trick legitimately.
    2
  1123. Oops, thanks for pointing this out.
    2
  1124. lol, yep
    2
  1125. As I was animating this one, I realized I strongly prefer vertical lines on maps to horizontal lines on maps. It’s such a shame that Taiwan just had to be oriented in the way it is. 😢
    2
  1126. There is a Kindle version. Not sure if that is an epub.
    2
  1127. I still do, and thanks!
    2
  1128. Thank you! You got this.
    2
  1129. I teach all of the game theory techniques as the course progresses. You can start watching immediately and it will be fine.
    2
  1130. Yep, he’s there
    2
  1131. Second...
    2
  1132. @cmlspice We'll do that in the video with continuous offers. Here, while technically an equilibrium, it isn't a very sensible choice for Tommy, which is why we should not expect that outcome.
    2
  1133. My homework set for this covers when two get taken away each time and when they both get to go back and forth for a certain number of offers. I will be covering these in future videos. But first we need backwards induction, which is something we haven't covered yet. Interestingly, though, when you cut in half or take away two each time, you get Rubinstein bargaining, which I alluded to in the video. Insightful thinking on your part.
    2
  1134. @laz3e Search "stag hunt game theory 101" on YouTube. =)
    2
  1135. @MrYakushi12345 Good response.
    2
  1136. I haven't been following this much over the last few years, so nothing new for me to add!
    2
  1137. In a word, yes.
    2
  1138. Did they link this or something?
    2
  1139. Nah I am just a dog who worked very hard to speak like a human…
    2
  1140. Second and fourth!
    2
  1141. +Jack Zhang Haha. Casey's version of the class is really different from mine, but good luck nevertheless!
    2
  1142. @sn3akyp3te No, you might get a different answer.
    2
  1143. Note that if player 2 cannot make that commitment, player 1 will certainly choose up, and player 2 will earn 1. In contrast, if she can make that commitment (perilous as it is), player 1 is forced to go down, and she receives 2 instead. So the only way she can improve her welfare is to make that commitment. And given that she has made the commitment and player 1 has responded by going down, she has no reason to overturn the commitment. So the strategies are stable, just as Nash equilibrium requires.
    2
  1144. You're back!
    2
  1145. +Ibrahim Alallaqi It's hard to give an absolute answer on that kind of question because you can always DeMorgans a conclusion to make negations appear or disappear.
    2
  1146. What you said is right.
    2
  1147. That’s Austria, but they are so similar I can understand the confusion.
    2
  1148. +Peter Velzen The response from +SlackwareNVM is right
    2
  1149. https://www.youtube.com/watch?v=XGc2UqQR9J8
    2
  1150. Thank you!
    2
  1151. Thanks!
    2
  1152. Both of these games pre-date me, though I made some modifications to the normal version of the letter scramble video to add a tenth word to partially hide how these are essentially the same game.
    2
  1153. I did one a while back: https://youtu.be/h7Z9Tb1kQ3A I have more ideas on this, but that video wasn't very popular, so I am not planning to revisit the topic any time soon.
    2
  1154. What do you mean? Like fantasy sports?
    2
  1155. If you can't wait until next week, part two is here: https://www.youtube.com/watch?v=bV_jdb5GDRA
    2
  1156. Good news! Most of the class is already up: https://www.youtube.com/playlist?list=PLB5965C13F4B0B2DA I'm just going through and updating things where necessary.
    2
  1157. Thanks!
    2
  1158. Those fields are just too damn long.
    2
  1159. Wait, is it a head of lettuce now?
    2
  1160. Working on it…
    2
  1161. Don’t mind me, I am just working on a blog post about all of the things that House of the Dragon has done wrong.
    2
  1162. Well done! I thought this would be the hardest one so far, so extra good job on your part.
    2
  1163. You were second, but this one is hard enough that you still deserve a shoutout!
    2
  1164. From what I did in the past two videos, I had the proposer making an offer. To be clear, an "offer" and a "demand" are identical because the other player has to receive the remainder. So "offers" map directly to "demands" and vice versa. I go back and forth on whether to use demands or offers in my research, depending on which is more useful for cancelling out numbers later on. It's admittedly confusing, but you get used to it pretty quickly.
    2
  1165. Definitely need to do a crossover episode at some point!
    2
  1166. We didn't assume the prisoners couldn't work together in a prisoner's dilemma. That was a _result_ of the strategic situation. Players couldn't credibly commit to cooperating there because of their own individual incentive to take the non-cooperative action. Here, cooperative outcomes are possible because if I want to cooperate with you if I know that you will cooperate. That wasn't true in PD.
    2
  1167. +linh trang pham You're welcome!
    2
  1168. That works because it's a zero sum game. So if you know one player's payoff, you know the other. It wouldn't work more generally.
    2
  1169. Not sure what you mean. I believe that sometimes people really do randomize. Outside of that, Harsanyi purification also works for me.
    2
  1170. Thank you!
    2
  1171. No, sorry. It would take forever for me to narrate it, and I don’t think there ohms be sufficient demand.
    2
  1172. BECAUSE I AM SAVING THAT FOR MY AUTOBIOGRAPHY :)
    2
  1173. DeMorgans all the things.
    2
  1174. That’s amazing! It is worth noting that the Supreme Court case he referred to was after the stop that I experienced, so what happened in the video can’t happen today.
    2
  1175. and round
    2
  1176. Was hoping someone would notice!
    2
  1177. I am the danger.
    2
  1178. TheLukeskywalker2 A few in the near future. Not sure what my time commitments will be past that.
    2
  1179. +TheLukeskywalker2 We're talking about the link in the video description, right? I'm have opened it on Chrome and IE without problems. I cleared cookies, so this shouldn't be a problem with it being a private page. I'm soooo confused.
    2
  1180. +vincentyification Really? It's working just fine for me.
    2
  1181. Your secret is safe with me 🙃
    2
  1182. "However."
    2
  1183. With the confirmed first comment!
    2
  1184. http://wjspaniel.files.wordpress.com/2013/12/pscir265-syllabus.pdf
    2
  1185. http://wjspaniel.files.wordpress.com/2013/12/pscir265-syllabus.pdf
    2
  1186. http://wjspaniel.files.wordpress.com/2013/12/pscir265-syllabus.pdf
    2
  1187. If they are playing the modified game and at least one of the players is playing the equilibrium of the modified game, then both receive 0.
    2
  1188. Second!
    2
  1189. I see what you did there
    2
  1190. I believe…
    2
  1191. I believe so
    2
  1192. I believe so…
    2
  1193. Do we think that? I mean, if the United States is the calling the shots, that sounds pretty good for Americans. But if it's someone else...well, that's pretty bad for Americans.
    2
  1194. +harryfakename Fascinating indeed. I would change my last name to "Australian Stumpy Tail Cattle Dog" for no other reason than to confuse the hell out of people. For the family pet, I would choose a beagle or Jack Russel terrier.
    2
  1195. Depends on the topic, but this is the most common one for conflict data: http://www.correlatesofwar.org/
    2
  1196. Can’t wait for the Dread Pirate Nash fanfics to pop up here.
    2
  1197. I'm not sure what you mean. Are you referring to a technical point about the equilibrium concept? It is true that there are multiple Nash equilibria for this type of game, but what I describe in the video is the unique subgame perfect equilibrium.
    2
  1198. YouTube now flags your comments on my dashboard with a purple heart icon that says "Top commenter: Received one of the highest number of hearts from you". =D
    2
  1199. Yep.
    2
  1200. Indeed.
    2
  1201. Thanks! I think I would be a good fit for Nebula. But this channel only truly took off three months ago, so I'm still fairly new to the content game.
    2
  1202. Ah, the joys of creative commons! =D
    2
  1203. Here's a link to the video where I talk about it. You can also find the original study linked from there. https://youtu.be/Y74I4lJ7aWk I haven't seen any polls with approval rating broken down by age, but that would interesting to examine if you know a source.
    2
  1204. That is incredibly generous of you. Thank you so much for contributing to the channel!
    2
  1205. I can confirm that the video has it correct. One way to see that it should be right as stated is because the numerator in the even period total is \delta x, and \delta x is the payoff in the first even period.
    2
  1206. Right. The lecture says "here's one thing terrorism does." It does not pretend to claim that "this is EVERYTHING terrorists do." I don't make that claim because it's the "safe" thing to do--I don't make that claim because it is the right thing to do. Analogy: I present a video on long division and then someone says "this video didn't cover differential calculus and is therefore bad."
    2
  1207. 1) The same assumptions must produce the same conclusions, though different people might choose different assumptions. 2) It's difficult to pass judgment on something that isn't transparent.
    2
  1208. I never made any blanket statements like that...
    2
  1209.  @PunmasterSTP  Based on the timestamp of the comment, I think it's this one? https://www.amazon.com/Bargaining-over-Bomb-Successes-Negotiations/dp/1108701841 Which is to say it worked out rather well. :)
    2
  1210. It isn't simultaneous. An easy way to check on that is whether you can flip flop the temporal ordering of the moves without breaking the game. Here, that clearly won't work because the seeker has to receive a signal (or not) based on the hider's move.
    2
  1211. And what an honor it is!
    2
  1212. Nope and nope
    2
  1213. Cannibal Island won last Friday's poll by a solid plurality. New poll tomorrow for Thursday's video!
    2
  1214. They are cannibals, not anarchists!
    2
  1215. Not sure what you mean. No one is actually dying when the game is played. It might help to think of it with just two cannibals. Cannibal #2 will definitely eat Cannibal #1 if given the option, so Cannibal #1 chooses not to eat you to protect himself.
    2
  1216. Just the time that the video will be posted
    2
  1217. I did a whole video on that about a month ago!
    2
  1218. You are correct. I really need to re-do this one...
    2
  1219. You could do it with that payoff as well.
    2
  1220. Fourth!
    2
  1221. I actually noticed this as I was recording, stopped to fix it, and then decided I thought it was more fun if I didn't!
    2
  1222. You're welcome!
    2
  1223. Thanks again!
    2
  1224. It certainly is fitting!
    2
  1225. Yep. That is one of my all-time favorite typos.
    2
  1226. I acknowledge you.
    2
  1227. Congratulations on being the first to find him!
    2
  1228. Thank you!
    2
  1229. “International.” The first T tends to disappear.
    2
  1230. Oh I know.
    2
  1231. It will be revealed in a couple of videos!
    2
  1232. I HAVE NO IDEA WHAT YOU ARE TALKING ABOUT 🤫🤫🤫
    2
  1233. For what it’s worth, when I first encountered Nim ~12 years ago, it took me a long time to figure out the solution too.
    2
  1234. Oops...
    2
  1235. Nice choice on the profile pic
    2
  1236.  @TheRoundhouseReport  Ah, it's a program called CamStudio.
    2
  1237. It's just PowerPoint
    2
  1238. Glad you like them.
    2
  1239. I don't know the exact answer to that question, and I am not sure the exact procedures on this are publicly known. Presumably the military has some sort of contingency plans to give the Speaker access to the nuclear codes quickly in the event of a war.
    2
  1240. Well, at a minimum, you have given me something to look for the next time I go through the Kremlin website’s photo archives.
    2
  1241. I think the issue that some have a hard time wrapping their head around is that variance in outcomes can only be attributed to poor play. This may seem straightforward in a game like this, but it may be more difficult to understand for something like chess. But, yeah, in the grand scheme of things, it's certainly more obvious (and more readily proven) than Nash's theorem. On the other hand, it's more than a century old, it predates the study of game theory, and it predates Nash's theorem by about 40 years. It's not like people were formalizing the study of games for a long time before encountering the result.
    2
  1242. There are a lot of similarities, but the number of restrictions on what "piles" you can take from in this game are big enough that I wouldn't put it into the same category. What's interesting, however, is that the optimal first move of the square game does turn it into "misère" nim, with two piles and unlimited choices from any given pile in a turn.
    2
  1243. And if we are playing optimally, it doesn't even matter!
    2
  1244. Your chances of winning drastically go down. (Obviously!)
    2
  1245. I believe it is the main photo of the Pearl Harbor attack on Wikipedia
    2
  1246. I believe it is the main photo of the Pearl Harbor attack on Wikipedia
    2
  1247. https://en.wikipedia.org/wiki/Ig_Nobel_Prize
    2
  1248. !
    2
  1249. Thank you!
    2
  1250. It’s the era-appropriate flag of South Africa
    2
  1251. @affablegiraffable I knew someone might think that $500,000 is the "right" answer because it is the expected value of the lottery 1, but I think X < $500,000 is far more sensible.
    2
  1252. +Nathan Chin At the very least, that makes a lot of sense when you are a short stack facing large big blinds.
    2
  1253. Unfortunately, it doesn't really translate well to videos. I did discuss the main mechanism from one of the chapters in this video, though: https://youtu.be/6wV2B1zgnNw
    2
  1254. Maybe! More likely is that I would add it as an extra topic of discussion when I compile all of these into a book.
    2
  1255. You are welcome a bunch!
    2
  1256. You could stick with Q instead, but that would be like using y to represent the negative version of x in algebra instead of just using -x-. This would be valid but unnecessarily complicated.
    2
  1257. Yep! It had started when I made this series, and it still continues to today...
    2
  1258. +asdas I hadn't heard of those axioms before, but it appears that Independence lumps the three of those together under one rule.
    2
  1259. +Putione That looks like it would follow from independence. You'd have to do some funky comparisons with those degenerate lotteries, but you should be able to get it from that. (It's also true that expected utilities exhibit this property. It's not completeness, transitivity, or continuity causing it, so it must be independence.)
    2
  1260. Thanks!
    2
  1261. Meliora!
    2
  1262. Yes, and beer-quiche is two videos away.
    2
  1263. I missed an opportunity there.
    2
  1264. I started recording at 7 am this morning. Definitely noticed the same thing when I was doing the post production!
    2
  1265. Straight from the Kremlin's website.
    2
  1266. @ithinkimemo04 "Winning" means doing the best you possibly can. Here, the best you possibly can do is break even with your opponent. (Conceivably, if your opponent is stupid, you can also win if you play 5 and they play 1-4.)
    2
  1267. @ICarnag3I Mostly self-taught, and I had taken a graduate level game theory class when I started these videos.
    2
  1268. @nahaymath mind DOT ucsd DOT edu has a complete intro course. It was my undergrad course.
    2
  1269. @davidme123 It works for total game score too. Winning 350-300 is much better than losing 500-400.
    2
  1270. Glad you enjoyed it!
    2
  1271. The digital version is $5 and has been expanded since this video was published. It also now has a physical edition for $14.
    2
  1272. Thank you!
    2
  1273. 🤣
    2
  1274. What can I say, Ukraine put the Wright brothers to shame. 🤷🏻‍♂️
    2
  1275. Yes, once you get to college.
    2
  1276. Should be the same thing.
    2
  1277. You could think of the 2 meaning that they get to keep their investment.
    2
  1278. Not sure what you mean. Firm 1 earns 3 by entering and 2 by staying out. So, it enters.
    2
  1279. +ngyx57 One.
    2
  1280. +SurvivalBayArea I'm not sure what prompted this comment, but the font in the title slide and on the cover of the book is coincidentally the same font on the cover of Straight Outta Compton (the album).
    2
  1281. Thanks. I serve the Founders.
    2
  1282. Vote for Monday's video! Your choices include a trolley puzzle, a dice puzzle, avoiding eating a poisoned chocolate bar, and issues with expanding highways. https://www.youtube.com/channel/UCJDIGW0ywWw9Kh9_vtwqxXA/community?lb=Ugzx6AdLjvBvBd40d794AaABCQ
    2
  1283. Well, I have ideas of how to spice things up. 😁 Gotta start with the basics, though.
    2
  1284. That’s the Situation Room. I suspect that the names are there for the sake of the photos, because there is a good chance everyone at that meeting already knew everyone else.
    2
  1285. Yes, although sometimes there are shortcuts you can use with zero sum games that do not work generally.
    2
  1286. I'm not sure the game you are describing has an analytical solution. With continuous distributions, you set up a function to represent the proposer's expected utility for any given offer x, which looks like: (1-x)Pr[accept] + V(1 - Pr[accept]) where V is the proposer's outside option value. You get the probabilities by going through the cumulative distribution function of the probability distribution. After setting that up, you take the derivative with respect to x, set it equal to 0, and solve for x. (This is standard calculus optimization.) That gives you the proposer's best offer amount. This is easy to do with simple probability distributions, like a uniform. I'm not sure you can get an analytical solution when you take the derivative when you have a normal CDF floating around. The bright spot is that a solution still exists and is unique. That much I do know. This will be true for any distribution function with an increasing hazard rate.
    2
  1287. Civil Wars MOOC (#12): The Risk-Return Tradeoff =)
    2
  1288. Certified first!
    2
  1289. +Eugene Poubelle Premises should be treated as true. In reality, all proofs are conditional proofs of sorts. The premises are the "if" parts of the statement. You are showing that IF all the premises hold THEN the conclusion does as well.
    2
  1290. +christian enriquez Doesn't look like it. All the premises are conditional statements---that doesn't really give you anything to work with.
    2
  1291. The textbook is basically a written version of these lectures with a lot more examples.
    2
  1292. #h2p
    2
  1293. Thanks!
    2
  1294.  @PunmasterSTP  During my final year of grad school, I spent about half my time in Buffalo, mostly in the Amherst area. I thought it was nice, but obviously the weather can be brutal.
    2
  1295. Hi there hello
    2
  1296. Kinda. I watched the documentary years ago. I made the Tasha joke off hand. Then I realized that Google Trends would be a useful way to illustrate the importance of Kharkiv versus Chasiv Yar. Then I saw the West Virginia thing, I needed some accompanying imagery, and Moundsville was an obvious place to go.
    2
  1297. You should watch until the end. :)
    2
  1298. (1-p)*(-.2) = -.2 + .2p, right? Distribute the negative?
    2
  1299. Thanks!
    2
  1300. Yeah, I thought (1) was really neat the first time I learned about it, and it's one of my favorite lectures to teach IRL.
    2
  1301. Thanks! I have a bunch more in mind on current events, but the next one probably won't come out until next week.
    2
  1302. Thank you!
    2
  1303. Thank you!
    2
  1304. Thank you!
    2
  1305. Good thing I'm not actually paying you $999.39!
    2
  1306. Fortunately, given the dollar values on the board, it is still the Jeopardy round. Ken will forgive me. Now if this were the Double Jeopardy round...
    2
  1307. Thank you so much!
    2
  1308. There’s no Patreon
    2
  1309. Oh wow, I really do!
    2
  1310. Dammit!
    2
  1311. Hope you enjoy it!
    2
  1312. Lines on mobilization dimensions aren't good enough???
    2
  1313. Yep, unfortunately there is a dearth of free use photos of large groups of Iranians. 🤷🏻‍♂️
    2
  1314. Both?
    2
  1315. It won't happen. It's hard to believe the Soviet Union and United States really tried playing chess with the world not too long ago. China and the U.S. (more or less) have it figured out now--it's much easier to buy someone off than it is to fight wars.
    2
  1316. It purely depends on what you are interested in. How Ukraine Survived is a bit more of a relaxed reading experience. It is longer, but it does not require as much self-thought. What Caused the War is a deeper dive into the logic of why wars occur more generally. You will want to stop, think, and internalize more of the steps than with the other book.
    2
  1317. What a very generous donation, thank you so much!
    2
  1318. Yep. The military treatment was distinguishable from zero, the sanctions treatment was not.
    2
  1319. Beep boop oopsy
    2
  1320. That's weird. It doesn't do that for me when I open up a private tab.
    2
  1321. Actually, your comment appears first on my end!
    2
  1322. Correct. This is an older version of this series. If you want to learn more about repeated prisoner's dilemmas, you should go off a different playlist that starts with this video: https://www.youtube.com/watch?v=CO3-796fGv8
    2
  1323. That was a looooong time ago.
    2
  1324. I like it.
    2
  1325. Okay, maybe it's a bot. There was a downvote almost as soon as I published today's video.
    2
  1326. Interesting video! I don't remember too much about where all of the materials went. But at least some of it went to U.S. labs for testing, which makes sense---this was an opportunity to obtain some empirical evidence about the dangers of dirty bombs.
    2
  1327. Whoops!
    2
  1328. Not in my heart you're not.
    2
  1329. First comment!
    2
  1330. Either seems like a fine interpretation. The key is that, whatever the enjoyment is, you can't retroactively take away that day's value. But having received that day's value does not guarantee that you will receive the same value the next day.
    2
  1331. As soon as I finished recording, I regretted not saying "Putin is dying, but it's not clear if he's dying any faster than the rest of us."
    2
  1332. +Nicholas Haley It is a matter of taste. One adherence to disjunctive syllogism is that it there must be the negation of exactly what appears on the left side of the disjunction. (This is what you did.) But if you get out a truth table, disjunctive syllogism works the same if the left side of the disjunction is a negation and you have a line with the non-negated left side of the disjunction. (This is what's in the video.) If you are taking a class, check with your professor to see what is allowed for the purposes of grading.
    2
  1333. My voice got destroyed filming the last one and is still recovering
    2
  1334. That may be the case, but congratulations on moving into first place.
    2
  1335. But if player 1 is always choosing down, then player 2 should switch to left. The MSNE is the only set of strategies that breaks this cycle.
    2
  1336. It's algebraic manipulation of the previous line. Nothing fancy.
    2
  1337. Works the same way (if an MSNE exists).
    2
  1338. The most recent ones should, but that comes with the caveat that trying to ascertain accurate numbers for a politicized topic is difficult.
    2
  1339. It’s just how I talk. Sorry. 🤷🏻‍♂️
    2
  1340. =)
    2
  1341. Indeed!
    2
  1342. Thank you again!
    2
  1343. In what you described, tit-for-tat is a Nash equilibrium but not subgame perfect. The previous video explains this: https://www.youtube.com/watch?v=_BbFXgRjEcU
    2
  1344. Yep, that's a fun demonstration. I sometimes do it in my class after I teach this game.
    2
  1345. The setup for the paradox is a collective action problem (that is, a generalization of a prisoner's dilemma that allows for more than two players). There is a ton written on collective action problems, so you could begin your search there if you are willing to zoom out a little bit.
    2
  1346. Maybe. I have something planned for Taiwan and semiconductors. I am not sure if Pelosi is a part of that hook or if there is a different angle. Need to observe a little more with what happens next before I can say anything intelligent about it.
    2
  1347. It really is. The level of sanctions pre-February 2022 was not nearly as strict as post-February 2022.
    2
  1348. Also extremely generous, thank you very much!
    2
  1349. Apparently he liked to go to local DDs whenever he was traveling abroad as Secretary of State.
    2
  1350. Because it is!
    2
  1351. Contact info is in the about section: https://www.youtube.com/c/gametheory101/about
    2
  1352. I just wanted to say that YouTube did not send me a notification for this one, and I was worried that your streak was broken!
    2
  1353. It's on the secondary channel!
    2
  1354. Third =(
    2
  1355. From the second line to the third line, multiply everything by (1-d). The left hand side becomes just 3. The right hand side becomes 4/(1+d) + d /(1+d). The rest is easy. The confusing thing here is that (1-d)/(1-d^2) = 1+d.
    2
  1356. Quite impressive to find this given that it's still unlisted!
    2
  1357. Oh my bad
    2
  1358. I don’t know any specific channels that talk about this, but you’d be looking for the “comparative politics” subfield.
    2
  1359. Attended? I graduated with honors! You should see me with a needle.
    2
  1360. Spaniel. Just plain, simple Spaniel.
    2
  1361. Me? I am just a simple tailor.
    2
  1362. Yes, basically every photo of the US military in my videos comes from the DoD archives.
    2
  1363. Not sure I understand your question!
    2
  1364. Thank you!
    2
  1365. Thank you, as always!
    2
  1366. Thanks, and thank you for subscribing!
    2
  1367. You're always welcome!
    2
  1368. There's always a chance I can do that in another video!
    2
  1369. You're welcome as always!
    2
  1370. Fourth =\
    2
  1371. @FilthParade Players maximize their own payoffs. They are only concerned about their opponents' strategies insofar as it affects which strategies they play. You are thinking of zero sum games, where the payoffs in every cell sum up to zero, i.e. if my payoff is X, yours is -X. This is a special class of games that I don't really focus on.
    2
  1372. @CogitoErgoCogitoSum Not entirely sure what you mean here, but in mixed strategy Nash equilibrium, both players are completely indifferent about which strategy they play or any probability distribution between the two. It sounds like you might want to refer back to pure strategy Nash equilibrium, in which your strategy does depend on what the other player is doing.
    2
  1373. @swaine55 You have to consider all combinations of mixed strategies, which is quite a headache.
    2
  1374. @mrosendal Unfortunately, eliminating strategies like that does not preclude the possibility of MSNE. You can only really do that for strictly dominated strategies.
    2
  1375. @mrosendal I mean, you can still do it as a function of four equations. Set the three utilities equal to each other and then write out the utilities as a function of \sigma_{up}, \sigma_{middle}, and \sigma_{down}, and then substitute \sigma_{down} = 1 - \sigma_{top} - \sigma_{middle}. But, yeah, it's a mess.
    2
  1376. Yup, that's a mistake. I suggest you hop over to the updated playlist. Better production quality, fewer mistakes: https://www.youtube.com/watch?v=aa8USttcDoE
    2
  1377. Thanks!
    2
  1378. Much appreciated!
    2
  1379. Ugh. I screwed that up.
    2
  1380. Correct. Rival and excludable are continuous concepts, and things like public goods and club goods are simplifications for ease of analysis. Also, I really did think I had a spider on my screen for a moment.
    2
  1381. Give me 10 minutes...
    2
  1382. I’m not sure when I will do another one like this, but I have the full classes that I teach IRL as playlists on my channel page (e.g., game theory 101, international relations 101).
    2
  1383. Yep, thanks for pointing that out.
    2
  1384. That's basically the right interpretation. Each of the probabilities calculated in the video are the "breakeven points" for each of the actors. If the other person chose a strategy slightly more often that what was calculated, the other would have a singular preference for one of their strategies. If you haven't seen mixed strategy equilibrium before, it will definitely help to watch those parts of the course playlist: https://www.youtube.com/watch?v=fvEQujUcPv4&list=PLKI1h_nAkaQoDzI4xDIXzx6U2ergFmedo&index=7 https://www.youtube.com/watch?v=aa8USttcDoE&list=PLKI1h_nAkaQoDzI4xDIXzx6U2ergFmedo&index=8
    2
  1385. Snake?
    2
  1386. Second ain't bad...
    2
  1387. I could see that being a problem. The difference here is still a surplus of time. Even if they don't think, say, a tank can cross one of their pontoon bridges, you can always just drive it into the river or explode it in some other way.
    2
  1388. Italian Job!
    2
  1389. Probably not given that it appears to be a misfired Ukrainian interceptor. I might do something about Article 5 more generally at some point, though.
    2
  1390. Thank you so much!
    2
  1391. Another time, I promise!
    2
  1392. Thank you again!
    2
  1393. Solving that isn't too bad. It ends up turning into just a 2x2 game where if you always practice and kick in the same direction. The same sort of mixing needs to be done in equilibrium, and from there you can calculate the probability of a goal.
    2
  1394. Thank you again!
    2
  1395. Ah, gotcha.
    2
  1396. As in a probability came out as above 1 or negative?
    2
  1397. Nope. If I know your value is $10 and mine is $100, every extra dollar I bid beyond $10 unnecessarily gives ten cents to the house. I can therefore profitably deviate.
    2
  1398. Hmm, I might do something with the Shapley–Shubik power index for the puzzles series, but likely not anything on Shapley values.
    2
  1399. Start with this one and work your way forward: https://www.youtube.com/watch?v=qwN55kzmojM&list=PLKI1h_nAkaQoDzI4xDIXzx6U2ergFmedo&index=44
    2
  1400. I could change that, but I have already recorded a bunch of these. It will be awhile before you see the difference.
    2
  1401. Nice!
    2
  1402. I'm not a chess expert, so I can't do that! Militant Competition had a bunch of delays on the production end. It looks like it will be coming out this week, at which point Amazon (and others) will have it. When it is released, I will have a puzzle that is based on something from the book, so you will know it is out at that point.
    2
  1403. So say we all
    2
  1404. Thank you!
    2
  1405. Lots of lines coming on Tuesday, my friend.
    2
  1406. Still not here, sadly!
    2
  1407. My wording was poor and a not so fun version of the pronoun game. “Their” meant “Haley and Biden” not “Haley and Trump.” That’s why Haley and Biden appear together during that sentence. It is also why a race between Biden and Haley would not matter much for Ukraine policy.
    2
  1408. My wording was poor and a not so fun version of the pronoun game. “Their” meant “Haley and Biden” not “Haley and Trump.” That’s why Haley and Biden appear together during that sentence. It is also why a race between Biden and Haley would not matter much for Ukraine policy.
    2
  1409. In that case, the proposer can demand everything/offer nothing. The other side is willing to accept all proposals because its war value is negative.
    2
  1410. https://www.youtube.com/watch?v=Zbr0c5QCpos
    2
  1411. +neil lang Whether the statement is true or false depends on the combination of simple sentences at the beginning. For example, ~P v (P ^Q) is true when P and Q are both true but is false when P is true and Q is false.
    2
  1412. Yeah, that looks like it would be a really good intuition if the goal was not to bomb the final square. I haven't solved it like that before, and I wonder if there is a way to force evens like you stated.
    2
  1413. Well, either a move is a winning move or it isn’t in games like these. (No private information, no randomness.) So it is true that the second player wins if the first player does not play the best strategy, though that does not mean too much. If one generalized this game to being some number of rectangles with some type of dimensions, I suspect that (1) the first player should win most of the setups and (2) there are a lot more moves that can cause player 1 to lose than win, so “should win” and actually win in practice are two very different things.
    2
  1414. Not sure what you mean. If you are watching from the main playlist, everything there is the most up-to-date version of the class. Whenever I teach it in person, I usually update a handful of videos. That's why some of them date all the way back to 2012 and some are as recent as 2021.
    2
  1415. Third, sorry.
    2
  1416. Eighth, sorry!
    2
  1417. Second, but this apparently was a tough one, so you deserve an acknowledgement!
    2
  1418. Whoa, that's crazy.
    2
  1419. That's not an equilibrium because both can profitably deviate to producing two units and increase their profit from $7 to $10. Actually, once you get the game down to just one and two for each player, it's a prisoner's dilemma. So if the logic is a little confounding, you should check out that video again.
    2
  1420. Thanks!
    2
  1421. Yeah I hear it a little bit!
    2
  1422. Mostly spit-balling here, but Russia's nuclear arsenal is much better institutionalized than, say, Pakistan's. This carried over from the Soviet era, when leader transitions weren't always smooth. So, yes, it would be a lingering concern. It just wouldn't be as pressing as if this were to happen in Pakistan or North Korea.
    2
  1423. Third!
    2
  1424. https://www.youtube.com/@LinesonMapsExtra
    2
  1425. Hard to do much better.
    2
  1426. I still use the Cuba example in my class. There's a teachable point that Obama did it after he was unable to run for reelection and right after the 2014 election---minimizing the damage to the Democratic party.
    2
  1427. Writing it as .333.... is fine. (Not 1.333..., though!)
    2
  1428. It looks like it's on Amazon and eBay and elsewhere. But it is 100% a math book, so be forewarned.
    2
  1429. Please vote on Thursday's video! An interesting variant on tic-tac-toe versus why people think they are a good drivers: https://www.youtube.com/channel/UCJDIGW0ywWw9Kh9_vtwqxXA/community?lb=Ugkx56jX6EQfOyfO28LorPjkYbW0cX6iBslg
    2
  1430. Each person can only control their action. It is consistent for me to want to choose west if I anticipate you choosing east, and vice versa. We are maximizing our individual outcomes---the only things we can control---even if we fail to maximize a group objective. It's the game theory equivalent of "bad things can happen because we expect bad things to happen." If that doesn't convince you, think about this. Imagine that there were 500 people on each of the north and south tracks and 1001 people on the center tracks. The best outcome for us is to still go north/south. But if you suspect that the other person may choose to go center instead, your choice is going to cause 500 extra people to die. And if I suspect that your suspicion is going to cause you to want to hedge your bet by going center, then now I want to go center. That just reinforces your suspicion to go center. And now we are stuck with a slightly worse outcome than the alternative.
    2
  1431. Wow. Just wow.
    2
  1432. Any idea what percentage have actually won?
    2
  1433. Thanks for the catch. Not sure if I will fix this with annotations or reupload...
    2
  1434. If the goalie's expected utilities for diving left and right are not equal, then the striker's strategy is exploitable. Essentially, by making the goalie indifferent, the striker ensures that he can't get screwed over. The same is true in reverse.
    2
  1435. Sort of. It's a necessary condition of a mixed strategy Nash equilibrium.
    2
  1436. If the goalie's expected utilities for diving left and right are not equal, then the striker's strategy is exploitable. Essentially, by making the goalie indifferent, the striker ensures that he can't get screwed over. The same is true in reverse.
    2
  1437. https://www.youtube.com/@LinesonMapsExtra
    2
  1438. Don’t give me ideas…
    2
  1439. https://www.youtube.com/@LinesonMapsExtra
    2
  1440. You are welcome!
    2
  1441. https://www.youtube.com/@LinesonMapsExtra
    2
  1442. https://www.youtube.com/@LinesonMapsExtra
    2
  1443. https://www.youtube.com/@LinesonMapsExtra
    2
  1444. https://www.youtube.com/@LinesonMapsExtra
    2
  1445. https://www.youtube.com/@LinesonMapsExtra
    2
  1446. https://www.youtube.com/@LinesonMapsExtra
    2
  1447. https://www.youtube.com/@LinesonMapsExtra
    2
  1448. https://www.youtube.com/@LinesonMapsExtra
    2
  1449. https://www.youtube.com/@LinesonMapsExtra
    2
  1450. Right. There's also a trick for MSNE with weakly dominated strategies that is covered the third unit.
    2
  1451. +ngyx57 Two: <yes, yes> and <no, no>.
    2
  1452. I think you were the only one to find him!
    2
  1453. Second isn't bad!
    2
  1454. Second =/
    2
  1455. Second =/
    2
  1456. @Pallerim Pure.
    2
  1457. Choo choo, you're a winner
    2
  1458. Second ain't bad
    2
  1459. Yes. Sports often provide great applications. Search YouTube for "game theory 101 penalty kicks" for a soccer example or "game theory 101 breaking balls" for a baseball example.
    2
  1460. I know. It's the Immortal Regiment march. Putin is in the front row.
    2
  1461. Yeah that one took a few takes to get right. The joys of hypotheticals in English…
    2
  1462. Thank you!
    2
  1463. Because the columns are player 2's strategies, not player 1's strategies. So player 2 doesn't care that center is better than left for player 1. She only cares that left is better than center for her.
    2
  1464. I forgot it was in there. But if I had to guess, that is likely the first time I saw a depiction of it too!
    2
  1465. Hmm, it looks good to me. One reason for the discrepancy might be following where the parentheses are paired with, and certainly the formatting of the notation is not making that easy.
    2
  1466. Yep, that will be after the Stackelberg stuff is done.
    2
  1467. Super generous, thank you!
    2
  1468. No, that would still remove Nash equilibria. Look at the "odd rule" video later in this playlist. It's weird, yes, but it's important if you want to carry out some sort of punishment to your opponent.
    2
  1469. We’ll be opening for ABlinken in no time.
    2
  1470. “It” refers to Ukraine. Ukraine’s demographics are worse.
    2
  1471. I don't think there is much similar to the videos other than they are both about the same topic and both discussing game theory. In any case, that video uses an escalation style game that was popular in the 1980s and doesn't even solve it right. ¯\_(ツ)_/¯
    2
  1472. Link? These types of lines are common within the study of crisis bargaining, but I can assure you that I (who does the academic study of crisis bargaining for a living) was doing this on my own.
    2
  1473. Do you have the more specific math on tanks and ground pressure? I tried looking up some specs and it was way harder to get than I thought it would be.
    2
  1474. Is that a new thing, or have they always been like that?
    2
  1475. Check out the next video on pure strategy Nash equilibrium!
    2
  1476. Entirely different, yes.
    2
  1477. A damn cloud. More specifically, sunlight reflecting off a cloud.
    2
  1478. Thanks!
    2
  1479. Yeah, I have taught the advanced game theory class and a class on international institutions.
    2
  1480. I've never taught a grad class, so I'm not exactly sure what you mean.
    2
  1481. Within crisis bargaining, there are a couple: https://doi.org/10.1093/isq/sqz050 https://doi.org/10.1017/S002081830999018X There's also a larger literature on economic sanctions that use formal models.
    2
  1482. Legend has it that his remains are buried under the tree outside the political science department.
    2
  1483. Nope, that was just me being dumb with the animation!
    2
  1484. Thank you!
    2
  1485. Because *family*.
    2
  1486. Hello Sir General!
    2
  1487. https://www.youtube.com/watch?v=tGcg77yr4hI&index=10&list=PLKI1h_nAkaQq44yiYz_5eNByopc_D_U-G The comments have an explanation for what happens in the infinite horizon case.
    2
  1488. To be clear, P1 doesn't know the result of the coin flip here. Only P2 does, though it doesn't actually matter in this example. You are right that P1 knows that P2 knows. But it has to be the case that there is some probability that P1 knows that P2 knows, otherwise you don't have a define-able game. There has to be some positive probability that P2 knows the result, otherwise you are asking for P1 to condition on a 0 probability event, which doesn't make sense. That all being said, you could define a new game where P2 receives information about the coin flip with probability p. Thus, P1 doesn't know whether P2 is informed or not. In that case, there would be a cutoff on the probability that P2 is uninformed that would allow P1 to choose to play despite the fact that he will lose to the informed types. So knowing for sure that P2 knows is not necessary for more information to hurt P2.
    2
  1489. There is a grim trigger-esque efficient equilibria in which both players play the "cooperative" strategy in every period and deviate to the noncooperative strategies if either fails to cooperate in any period. https://www.youtube.com/watch?v=8jBouAQt9EY&list=PLKI1h_nAkaQoDzI4xDIXzx6U2ergFmedo&index=59
    2
  1490. I think you are looking at French Guiana. (It is owned by France and is accordingly colored to match it.)
    2
  1491. Yes. I use simple sentences in the description of all of these rules, but you can apply them with complex statements just as easily.
    2
  1492. If this were a two player game with simultaneous decisions, 250 from each is in fact the Nash equilibrium. So that counts for something!
    2
  1493. Thanks!
    2
  1494. Haha! GT > YOLO.
    2
  1495. Thanks. Need to make some changes to the IR101 playlist before I start teaching the class IRL in the fall. After, I'll be doing a course on bargaining theory in conjunction with the release of a book on the subject.
    2
  1496. At most places, microecon won't be useful for IR. The way I teach this undergrad class matches what you would encounter in a graduate program, but most universities severely tone down the technical parts for undergraduate courses. So would microecon be good for your general education on the subject? Yes. Will it be useful to do well your class? Probably not.
    2
  1497. That is correct.
    2
  1498. Looks right to me.
    2
  1499. +Jasper Vandenbrande I think I understand what you are asking, and it is a fairly common question. Any preference for altruism or hatred of the other player is already built into the payoffs. Thus, you don't have to think about these things once you are solving the game, otherwise you are essentially double-counting the preference. I talk more about this in the textbook and leave it out of the videos since it is more of a modeling issue than a mechanical one.
    2
  1500. It's identical to the game from the mixed strategy algorithm video, so I'd suggest going back and rewatching it.
    2
  1501. There is no "official" notation, so I can't give you an answer. (If you look at most published papers, they will usually write out the equilibrium in words and avoid unnecessary notation.)
    2
  1502. +Marissa J I'm not sure I understand your question. Escalate is part of the SPE.
    2
  1503. Interesting idea! I will add it to the list of things to do.
    2
  1504. Certified first!
    2
  1505. Sixth, sadly.
    2
  1506. There is nothing wrong with steps one and two. The rant is about steps three and four.
    2
  1507. Hi there hello!
    2
  1508. Deep cut right there.
    2
  1509. Publishing non-basic models requires some advanced mathematics---about on the order of an undergraduate minor in the subject. More is better for some applications.
    2
  1510. What kind of class?
    2
  1511. They all work for me...
    2
  1512. So, we're getting to that. =)
    2
  1513. The closest control for that in the data would be a measure of the country's autocracy/democracy score, which I think would be correlated with anti-nuclear regime preferences, though not strongly so. You are right that the true "cost" of nuclear weapons the theoretical model cares about is a combination of physical ability and political willingness, so the empirical model is only capturing half of it. Unfortunately, there wasn't (and still isn't) a good measurement for nonproliferation norms. I know someone is working on this, so it may be possible to revisit the question in years to come.
    2
  1514. https://en.m.wikipedia.org/wiki/Patriarch_Kirill_of_Moscow
    2
  1515. Winning.
    2
  1516. Cool. Good luck!
    2
  1517. I'm not sure what you are actually referring to, but let's take what you said as a given. Then this force is not a "police" precisely because it operates under contract...which is precisely the argument from the video. The world is "self-help"; if you want help, then it's up to you to get it, either by doing it yourself or hiring someone else to.
    2
  1518. Thank you as always!
    2
  1519. I appreciate you!
    2
  1520. I don't think the West's main mistake occurred mid-war. Obviously, there have been hiccups along the way, but the West is going to come out way better from this than Russia will. The main mistake was pre-war, when insufficient attention and support was given to Ukraine. Hindsight is always 20/20, but the West's focus pre-war was on solving insurgencies/civil wars. China was the only big focus internationally. It made sense to place emphasis on China, but that should not have come at the expense of completely gutting attention to Russia.
    2
  1521. Ah, the glories of the English language. "You get to (a-c)^2/4."
    2
  1522. Thanks!
    2
  1523. I am.
    2
  1524. Only played MGS1. Probably going to try 5 soon, after Zelda BotW.
    2
  1525. Go to my channel--the complete Game Theory 101 playlist is there. (It is also more recent and has better video quality.)
    2
  1526. Yeah...I changed the wording in the most recent series to avoid this exact problem.
    2
  1527. @1Themuffinman1 This is just a convention that existed long before I created the video. Personally, I think the "classic" prisoner's dilemma story is really silly, and there are plenty of better examples to use instead.
    2
  1528. Glad someone noticed. I went out of my way on that one…
    2
  1529. Thank you!
    2
  1530. That's a lot of heavy reading haha
    2
  1531. Rusko!
    2
  1532. A Hind D? Colonel, what's a Russian gunship doing here?
    2
  1533. $2000. I think I got the exact situation from today correct. I could be wrong. But it was egregiously greater than the superior wager, and this happens fairly often.
    2
  1534. I have actually wondered why this doesn't happen more frequently. The other guy could also reciprocate the next game; if he leads going into Final Jeopardy, he could bid enough so that he can't lose but you could tie. Both parties win.
    2
  1535. Bro, never skip math day!
    2
  1536. No way I was going to deny a good Wilhelm a moment in the spotlight!
    2
  1537. I fell for that one. Hard.
    2
  1538.  @rebekahfrogoso5326  That will probably get you to the right answer, but you should double check that firm 1 wants to produce 20 given that firm 2 is playing its best response to firm 1 producing 20.
    2
  1539. I don't know what to tell you---what the channel is now is literally what I do with my PhD on a day-to-day basis outside of YouTube.
    2
  1540. I sometimes encounter this as well, and not just on my own videos. I find it only happens on my phone, and I have no idea what it is on YouTube's end that causes this.
    2
  1541. You too, Mr. Estonian Flag with Eyes.
    2
  1542. I recommend they be shipped in cardboard boxes.
    2
  1543. Thanks, I went through a few iterations of the game before getting it that way.
    2
  1544. Thanks, but I would prefer the title Mr. Maps.
    2
  1545. Good question. The United States nays a lot of resolutions regarding general international cooperation. Without going to deep into the data, my guess is that Israel tends to vote yea on those.
    2
  1546. Oops, just added it to the video description.
    2
  1547. This is the weird thing about the game. The number of marbles that are in your opponent's hand determines how many you have to give to them. (See 2:33 time stamp.) If I were in charge of the world, I would change the rules to what you were thinking. It makes the strategic problem a little more interesting when the guesser does not have a clear incentive to put 10 in their hand.
    2
  1548. @DJTripleThreat78 All you need are cell formulas.
    2
  1549. I thought so too and then I discovered that, no, there was just a lot of selective breeding over the last few decades that removed the bitterness.
    2
  1550. There is some crossover, especially with the contest models.
    2
  1551. You're really getting into the deep cuts of this channel now!
    2
  1552. Ignacio Parellada Basically whatever I'm teaching about or have recently written a book on. Happy to have you here!
    2
  1553. Well, there are two ways to look at this: 1) When thinking about whether direct mechanisms are incentive compatible, the rules of the game are the rules of the game, period. So in the example, you get the stuff that the game master gives you, and there is nothing you can do to change that. This isn't because we are suggesting that we could replace real life interactions with the incentive compatible direct mechanism. Rather, the revelation principle gives us a way to neatly compact the otherwise (potentially) extremely complicated strategies of any given game. If this seems to only be of academic interest, you are right...so far. However, we can rewrite the revelation principle in a logically equivalent way. The next lecture does this, and we will see the absence of an incentive compatible direct mechanism means that certain outcomes are impossible to arrive at through strategic play, regardless of what the actual interaction is. This is definitely not purely of academic interest, as it says that some situations will inevitably end in war. 2) That aside, lying in that manner doesn't make sense. That would be like if strong Putin says "I am weak," and then is given a small portion of Ukraine, say Crimea. Then, the next day, he realizes he could get more through war, starts a conflict, and takes a larger portion, say Crimea and Donetsk. By lying, he doesn't get Crimea twice---he only gets it once. (That is, you can't get a war payoff and a peace payoff.) And if he was better off starting a war than taking the smaller amount of concessions, then he might as well have just told the game master the truth from the start so he could receive his war payoff.
    2
  1554. Well that is quite the commitment you just made for yourself!
    2
  1555. In math land, the red line is p and the white line is p - c, where p is the distribution of power and c is China’s costs. The red and white lines have to track with one another because they are both a function of p.
    2
  1556. Thank you so much! Very generous.
    2
  1557. Every information set that has zero probability of being reached is off the path. So based on what you wrote, it sounds like everything you are describing is indeed off the path.
    2
  1558.  @PunmasterSTP  Nope, I just think that it is more assessable than a lot of other textbooks. (But it is still fairly dense.)
    2
  1559. Start with Game Theory 101 (the book) then maybe switch to Game Theory Evolving when you want to get to the complicated stuff.
    2
  1560. Yep, that's right.
    2
  1561. That actually was Biden!
    2
  1562. Hmm, I am not sure what you are asking.
    2
  1563. This is why I like studying international relations. Limited to no external enforcement!
    2
  1564. If you want something technical, “What Caused…” If you want something that is easier reading, “How Ukraine Survived”
    2
  1565. Thank you!
    2
  1566. Thank you!
    2
  1567. It seems like you'd be interested in quantal response equilibrium: https://en.wikipedia.org/wiki/Quantal_response_equilibrium
    2
  1568.  @christianandhuman1008  Actually, yeah. It's worse than I thought!
    2
  1569. Nope!
    2
  1570. @OnAFirefly I very briefly said that punishment could mean exile, so I guess he could exile himself and save the rebels from making that step. But regardless, this prevents him from being willing to accept a bargain that puts the rebels in power, which is what drives the result.
    2
  1571. Player 1 can only change his strategy. Down is the best he can do in response to RR. He can't control player 2's strategy to shift her to playing RL.
    2
  1572. Yeah, it gets counted like that. It makes sense--the war was going on at the same time. It's worth noting that China "won" the war with a gigantic asterisk. Japan brutalized China during the actual conflict. Western allies defeated Japan, which in turn gave China a very costly "victory."
    2
  1573. This is the full playlist: https://www.youtube.com/playlist?list=PLB5965C13F4B0B2DA
    2
  1574. I spend way too much time on world leaders’ Flickr feeds…
    2
  1575. Your description of the exact survey is correct (and welcome!), but it is worth noting that a ranking like this implicitly asks whether you are better than average or not. So I think that the headline takeaway (which the authors say themselves: "In the US group 88% and in the Swedish group 77% believed themselves to be safer than the median driver") is not an unreasonable thing to report. You could also get distorted beliefs like what I show in this video across a broader range of values, but that would a lot more math without any additional intuition.
    2
  1576. Second, ='|
    2
  1577. Gotta save the best for last!
    2
  1578. Thanks and you are welcome!
    2
  1579. Sir, it’s spelt STILLERS
    2
  1580.  @apitk7229  Yep, the paperback is in within the link in the video description---just need to click on the option within the Amazon page.
    2
  1581. That’s amazing!
    2
  1582. +Marco Meerman Hey, just noticed the question. Probably missed it the first time around because the email notifications cut off after a few sentences. I don't actually understand your question. Could you perhaps give an example?
    2
  1583. chuvzzz I suppose you could here, but things would start to get messy when you apply replacement rules. For example, if you write P v Q v R and want to apply material implication, how would you do that? There is a way to do that, obviously, but it starts getting increasingly (and unnecessarily) demanding as the statements become more and more complicated. (The sentence P, for example, could just as easily be P => T. R could be R ^ S. And so forth.)
    2
  1584. Why don't you take a seat right over there?
    2
  1585. And first comment!
    2
  1586. Very kind again, thank you!
    2
  1587. Thank you!
    2
  1588. I literally ripped up a piece of paper haha.
    2
  1589. Verified first!
    2
  1590. That's exactly the question of the "Did Putin "Cause" the War?" video! It's also a big part of why the bargaining perspective has taken over the academic research on conflict. Those explanations tend to be better about explaining the timing of things. I really hope the news will calm down for a week so I can finally record it.
    2
  1591. Unfortunately, that would take me too long to record. If you have a newer generation Kindle, I have text-to-speech turned on for the book, so you could do it that way. For what it's worth, I was using text-to-speech a bunch to edit the book, and it did a really good job. The only weird thing I remember was it kept saying "messier" like the hockey player and not as "more messy".
    2
  1592. Ah, yes, penalty kicks are zero sum. I was thinking about covert nuclear proliferation when I said that it isn't.
    2
  1593. Yep, with the differences that (1) not all of the outcomes are equally weighted and (2) it is not a zero-sum game.
    2
  1594. Multiplying it means that (1) how much I view a loss from today's perspective into tomorrow is the same as (2) how much I view a loss from tomorrow's perspective to the day after tomorrow. If you subtracted some amount, eventually the value of the good would be equal to 0, which doesn't make sense. There is another type of repeated bargaining where each period of delay costs some fixed amount to both players, but it is much more difficult to solve the version of it with infinite counteroffers.
    2
  1595. Same process as always. Start at the bottom and work your way up. Doing this very quickly, I think Albert gets 1-d^2 and Barbara gets d^2. That's because Barbara takes the surplus (discounted down to d^2) in the third period. So Albert needs to give her amount in the second period for her to accept, which in turn means that he only needs to give her that amount in the first stage to get her to accept.
    2
  1596. They were more or less redos with a better microphone. I did comparative statics on penalty kicks and also the rule about two player, finite, symmetric, zero-sum games. That was about all the new stuff.
    2
  1597. Still hope so!
    2
  1598. I really hope I'm still me...
    2
  1599. All of these are already recorded, so can't do anything about it now! ¯\_(ツ)_/¯
    2
  1600. That's something I have been thinking about!
    2
  1601. The lines will return next video, I promise!
    2
  1602. Thanks for the algorithm boost! :)
    2
  1603. Thanks.
    2
  1604. It certainly goes both ways, and that's something I will talk about in the next lecture.
    2
  1605. I wrote it all, and probably spent way too much time doing so. 😅
    2
  1606. Oh my bad
    2
  1607. You bet!
    2
  1608. Okay, I skimmed that real quick and there wasn’t anything obviously wrong with your math. And this is a general problem with the even piece of information as you were speculating.
    2
  1609. It’s the same with or without replacement. I can’t comment on whether your justification was right, but your conclusion is!
    2
  1610. Thank you! I will consider it.
    2
  1611. Thank you so much!
    2
  1612. this is a reply
    2
  1613. Thank you!
    2
  1614. Thank you so much!
    2
  1615. Varsågod!
    2
  1616. Nope, just me. You can hear me breathing between sentences.
    2
  1617. Yinz!
    2
  1618. Just watched the episode today. I thought they were talking about autocratic leaders, not how many people Blight killed. 😅
    2
  1619. It’s an official U.S. military war game
    2
  1620. Pravda Pravda Pravda
    2
  1621. It is!
    2
  1622. Whoops, my bad.
    2
  1623. Neither was the U.S. government. Maybe they should employ you---you were the first to find him!
    2
  1624. That's a great connection! When I first wrote the paper that is connected to this, I had beer-quiche in mind.
    2
  1625. Didn’t know about that, thanks!
    2
  1626. I've thought a bit about doing this. The problem is that the actual calculations for those things are usually pretty involved and would only be well-suited for a traditional class on the subject. For what it's worth, I have another video talks about the motivating case for the Banzhaf power index: https://youtu.be/Mpd5Tps6ONg https://en.wikipedia.org/wiki/Banzhaf_power_index
    2
  1627. No, I just got sick...
    2
  1628. Ah, yes. It is now only on Amazon. Sorry about that!
    2
  1629.  @Math.Bandit  Right, raising the toll to being between $5 and $10 doesn't change the patient commuters' welfare. The impatient drivers could be made better off by a toll of $5, though, because it would keep all of the patient drivers out and be more than worth the cost of doing so. I guess one of the unforeseen problems of doing these "puzzle" videos is that the questions don't have as clear of meaning as "what is the equilibrium of this game?" so there is a level of precision that I am losing in this playlist.
    2
  1630. Vote for Monday's video! Poll here: https://www.youtube.com/post/UgwLp6DVZT_EBisHBiZ4AaABCQ
    2
  1631. Nice calculation! Those answers match what I have. It's surprising that your opponent is more than 10x better off going first than second.
    2
  1632. You can change the marginal costs around and redo the calculations to get the results. I have to do this in the book, so I can tell you what the general solution is in the book. Let v be the value of the prize, m_1 be the first player's marginal cost, and m_2 be player 2's marginal cost. Then 1 produces vm_2/(4m_1^2). Meanwhile, for any e_1 produced, 2 produces sqrt(ve_1/m_2) - e_1. (You can substitute 1's actual production into that formula to get what 2 will produce when they play.) When the marginal costs are equal, there is actually no advantage to player 1!
    2
  1633. Yeah, that's one of the ways they are used in the contest literature. The basic point in the book that I mentioned is that one group may overproduce so much that it keeps the other group from entering at all. From a consumer welfare standpoint, this is actually beneficial though. More effort is exerted from the "predatory" behavior than when there is active competition.
    2
  1634. Sounds like a giant headache of backward induction! I suspect that someone in the contest literature has answered that specific question, but it's vast enough that I don't know everything that is out there. The more general principle that I would recommend to a business leader who is the first entrant into a market is that they should produce more than what they would if the other entrants were arriving at the same time. There may be some apparent incentive to slack off (because you appear to be a monopolist) but that takes away your ability to strike first and deter others from challenging you.
    2
  1635. Sorry, but I have to. The majority of viewers of each video is new to the channel. You can always skip ahead.
    2
  1636. Unfortunately, my digital contract is exclusive to Amazon. You can always download the Kindle app to Apple devices, for whatever that is worth. Also, you had me really worried for a second that someone had pirated one of my books and was selling it on Apple. I even downloaded the app to figure it out. Then I discovered it was my dissertation. I didn’t know they bothered to have such an expanded distribution of it!
    2
  1637. Thank you!
    2
  1638. Thanks. I see that your parents also had good tastes in names.
    2
  1639. Thank you! Please leave a review on Amazon afterward. It really helps out.
    2
  1640. Do I qualify as “someone”? Why Russia Miscalculated in Ukraine: A Self-Inflicted Disaster in Three Acts https://youtu.be/8YkGrKQXZxE
    2
  1641. Once the war ends, I'm on it.
    2
  1642. Nailed it! Congrats on being the first.
    2
  1643. Thank you! Very generous.
    2
  1644. Thank you so much!
    2
  1645. Cheers!
    2
  1646. Yup. I'd check the playlist on the channel. Also, the end of each video sends you to the next.
    2
  1647.  @nicolastorres147  Exactly.
    2
  1648. Thank you for your generosity!
    2
  1649. It’s objectively the best one
    2
  1650. WHAT A COINCIDENCE
    2
  1651. You're the real MVP.
    2
  1652. It is!
    2
  1653. Fourth!
    2
  1654. Fifth!
    2
  1655. The payoffs of the MSNE of the stag hunt Pareto dominate the hare equilibrium (but not the stag equilibrium). That's the closest thing I can think of.
    2
  1656. This is correct, though I teach it this other way because I think it is more intuitive--you are calculating what actually happens in equilibrium.
    2
  1657. Wow, that is incredibly generous, thank you very much!
    2
  1658. Thanks!
    2
  1659. So close to being a coherent sentence…
    2
  1660. Yeah, there’s a chapter in there about personal benefits!
    2
  1661. Kind of. Here are some notes on the subject: https://economics.mit.edu/files/4711
    2
  1662. Thanks, glad you enjoyed it! Please leave a review on Amazon if you are so inclined. It really helps out.
    2
  1663. Second. Close!
    2
  1664. What's up with all the down votes?
    2
  1665. Oil prices have two countervailing effects, so it is hard to say. On one hand, it increases the cost of moving troops, ships, planes, etc. from point A to point B. This makes war less likely. On the other, it decreases the amount of trade two states conduct. This makes war more likely. So it is hard to say.
    2
  1666. Thank you!
    2
  1667. Very generous of you, thank you!
    2
  1668. Well now I am just going to have to delete this video…
    2
  1669. There’s a small bit of it between Bulgaria and Istanbul that is within continental Europe!
    2
  1670. Thanks, I try!
    2
  1671. Thank you so much!
    2
  1672. How likely is it that a group that has a vested interest in conflict would lobby for conflict? I think you answered your own question. :) (With the caveat that even that type of person would still be much worse off with a full scale war. Lobbying for lower level conflict is a different story.) To rephrase your question to give it a little more drama, how likely is it that war will actually arise between Russia/NATO or Russia/Ukraine? Wars are very, very low probability events, so you should almost always default to "probably not". Of course, the situation in Russia/Ukraine is bleak. If I had to guess where the next war would break out in the world, I would guess there. But that probability is still much lower than 50%. (Things that happen much lower than 50% happen quite often, of course. A soccer team losing 2-1 and coming back to win 3-2 doesn't really raise an eyebrow.) Russia and NATO are much, much further away from war than that.
    2
  1673. Thanks!
    2
  1674. Guess and check. You often have to fiddle around with them a bit.
    2
  1675. Can you give me an example of the problem you are thinking about?
    2
  1676. It keeps things cleaner when we start applying rules of replacement/inference to logical constructions. Basic arithmetic is clean when you have 1 + 2 + 3 since you can just replace it with 6. That's not really the case with logic.
    2
  1677. Looks good this time!
    2
  1678. Closest thing I have in mind is discussing Russia's failure to take an airport on the first day of the war and how that caused a big mess with Kyiv.
    2
  1679. Paperback copies should be available in the next couple of days!
    2
  1680. There is now!
    2
  1681. Actually, the reason it is like that is because I originally missed one of the issue areas when I first constructed the slide. I realized that fixing everything would be a lot more work than just rolling with the punches. That's how it ended up off screen!
    2
  1682. Ah, another game I would like to play in a world with infinite time. =/
    2
  1683. Meet me at grand central information desk at noon tomorrow?
    2
  1684. Outside of reading the research published on the subject, I'm not sure there is a good answer to your question. Part of the reason I created this series was to fill in the gap you are alluding to. You can look at my syllabus for the class to get a reading list: https://docs.google.com/document/d/1vYyWN5LdocTYeTomlx7qcnBaD33-oa0GyTlunT6v1Fk/
    2
  1685. The English statements allow for the possibility of paying fees for other reasons; M => ~F does not.
    2
  1686. +Syed Ameed It looks like your mistake is identifying simple sentences. We can't use F to represent "you are not paying absurd bank fees" because "you are not paying absurd bank fees" is not a simple sentence. "You are paying absurd bank fees" is a simple sentence, though, and we can turn it into the antecedent of the conditional by adding a negation. Thus, ~F at the start.
    2
  1687. No, but you are not the first person to suggest that.
    2
  1688. First question, yes: Game Theory 101: Infinitely Many Equilibria Second question, no: Game Theory 101: The Odd Rule
    2
  1689. Hmm, maybe it is a country issue? It looks available to me.
    2
  1690. Wow, that was incredibly generous. Thank you!
    2
  1691. You can always email me ideas!
    2
  1692. But if every game in the set is not of finite length, you have reached the same paradox in the opposite way (since that violates the construction of the set).
    2
  1693. @DamionCrane Dude, just go to my website.
    2
  1694. Nash equilibrium does not, but a refinement called "trembling hand perfect" equilibrium does. Not all Nash equilibria are trembling hand perfect, but the examples in this video are.
    2
  1695. Think of it like this. If we both wait, then we are back to square one at the next moment. Should I go? Should you go? That outcome is worse for me than if you clear the intersection from the start, because I know to just go immediately afterward.
    2
  1696. That's one of the many forms of material implication. p v q says that at least one of those must be true, so if not p is true then q must be true. Put differently, ~p -> q.
    2
  1697. Q1) The section on uncertainty addresses this. In short, the answer is sometimes. Q2) The section on Rubinstein bargaining addresses this. In short, the answer is no. (That was a much more useful short answer than #1!) Q3) No, what you are doing sounds smart.
    2
  1698. I will now feed the troll. Einstein, Fermi, Bohr, and von Neumann were all key Manhattan Project scientists. Einstein actually co-wrote the letter to FDR that got the program started. Fermi and Bohr are both famous in their own right. Von Neumann did a whole bunch of things: modeling explosions, creating computers, and launching game theory. In short, this is an objective claim. You are a troll.
    2
  1699. Unfortunately, if both of us pick Shirt, we are back to a tie! But yes, the joint wicketkeeper choice does determine how the game will end when the other three choices for each of us are identical. The 50/50 probability for Shirt ensures that neither one provides an advantage, though.
    2
  1700. Thank you!
    1
  1701. I stand corrected.
    1
  1702. Thanks!
    1
  1703. I have not personally, but some of my older videos have citations on Google Scholar.
    1
  1704. Ha!
    1
  1705. That is incredibly generous of you, thanks!
    1
  1706. Fourth!
    1
  1707. You bet!
    1
  1708. Third!
    1
  1709. And you succeeded in being first!
    1
  1710. Gern geschehen!
    1
  1711. Thank you!
    1
  1712.  @davidblack1639  That's okay, I can respect Lamar.
    1
  1713. Thank you!
    1
  1714. Yup, all the slides are from PowerPoint.
    1
  1715. Any decent one should.
    1
  1716. There's definitely some amount of power shift purely from the announcement. PRC wouldn't be able to undo it, so the preventive incentive is on whatever remains from actually coordinating forces. (That's what this video is about https://youtu.be/UHNG-FKcALM) The flip side is that because some of it is irrevocable, the declining state has an incentive to jump the gun on the announcement. So signaling that something like that could happen in the future is itself dangerous under that mechanism.
    1
  1717. Not hidden!
    1
  1718. Yikes
    1
  1719. Well earned, homie
    1
  1720. Not bad!
    1
  1721. Right there with you friend
    1
  1722. Verified first!
    1
  1723. Gotta do a favorite line color poll to settle this...
    1
  1724. Thank you!
    1
  1725. Hmm, which videos did you have in mind?
    1
  1726. Almost certainly not the last time I will make that mistake. Thanks!
    1
  1727. You might be the first person to have spotted him!
    1
  1728. Never watched Rugrats, did you? :)
    1
  1729. @centurion180ad That threat is not credible if Tommy wants to maximize his cookie output.
    1
  1730. @centurion180ad That outcome does not follow from the assumptions given.
    1
  1731. I try wherever I can.
    1
  1732. @centurion180ad We can put whatever assumptions we want to in the model. I talk about this at length in a video later in the lecture series. But it is still very much incorrect to expect a 50/50 split here.
    1
  1733. That's addressed here: https://www.youtube.com/watch?v=tGcg77yr4hI&index=10&list=PLKI1h_nAkaQq44yiYz_5eNByopc_D_U-G You would think it would work out that way, but it doesn't. Basically, you need the ability to make offers before you can actually capture surplus for yourself,
    1
  1734. @LimeGreenTeknii Think of it in terms of happiness. Sometimes, like in competitive sports, your opponent has to lose for you to win. But in other situations, like collaboratively hunting for large animals, both players can win.
    1
  1735. Some good news on that front: I have a short series on cheap talk communication planned for this summer.
    1
  1736. Thank you!
    1
  1737. Thank you!
    1
  1738.  @timowagner1329  Yes. I was very excited to play it and ended up disliking it quite a bit. =/
    1
  1739. Nice one!
    1
  1740. Never heard of that one before, but I enjoyed it!
    1
  1741. You were indeed the first. Congrats!
    1
  1742. Thank you!
    1
  1743. Winner!
    1
  1744. @jlmknight Thanks!
    1
  1745. @sn3akyp3te All the answers you get are "correct" in the sense that they are all pure strategy Nash equilibria. Buy my book on Amazon if you want to know more. ;) It's only $0.99.
    1
  1746. Very generous, thank you!
    1
  1747. QI is "chee." XI is the Greek letter, "zigh."
    1
  1748. Once the states actually have to face the bargaining frictions, then bargaining will break down. Here, they aren't actually facing any frictions in the second half of the game because the friction is at the beginning. But generally speaking, yes, the bargaining and war literature is trying to capture those other literatures in a single, unified framework.
    1
  1749. Don't think about multiple changes at once. If something is an equilibrium, then everyone should believe what is supposed to be happening in equilibrium is actually happening and play accordingly. Equivalently, if someone should not believe what is supposed to be happening is actually happening, then those strategies aren't an equilibrium.
    1
  1750. Thank you!
    1
  1751. I try!
    1
  1752. And first comment more generally!
    1
  1753. @greymattersblog Probably in the basics. There really needs to be an intermediate section, and this would be better placed in there. Maybe I will get to that over the summer.
    1
  1754. @Mariopartyrules Players maximize their utilities. They only care about others' insofar as it affects the others' strategic decisions. There is a subset of games called "zero sum games" that deal with the type of game you are thinking about, but they don't really exist in the real world.
    1
  1755. @Vonzi0000 This would be a case where eliminating weakly dominated strategies eliminates equilibria. There is no surefire method to know when eliminating weakly dominated strategies will cause a problem without manually checking. Removing strictly dominated strategies from the game is always the first thing you should do.
    1
  1756. Thank you!
    1
  1757. I think the premise of the question is where you are getting off track. Demanding p + c_B makes B exactly indifferent between accepting and rejecting. Being indifferent, it is optimal for them to take any action. It's just that there are no equilibria where B rejects with positive probability when A demands that quantity.
    1
  1758. No, just about all of the old videos have a corresponding video in the new series. The difference is that the new series is cleaner and more streamlined.
    1
  1759. This was part of an older series. Check my channel page or my website for the complete (ordered) series.
    1
  1760. YouTube blocks links from appearing in the comment section. If you go to my channel page, there is a link to the playlist below the showcased video.
    1
  1761. If you're liking these videos, I'd suggest going to my channel and watching the most recent version of the course. It's a bit more consistent and has much better audio.
    1
  1762. That's setting player 2's expected utility for keep going equal to her expected utility for swerving. This is the indifference condition that I mention in the ten seconds or so beforehand.
    1
  1763. That's correct.
    1
  1764. Yup.
    1
  1765. It's just on Kindle at the moment. (You don't need a Kindle device to be able to read it, though.) I'm going to try to expand it to a print version this summer.
    1
  1766. That's what I'm here for. =) Notation rarely helps.
    1
  1767. No, keep watching and you will find counterexamples.
    1
  1768. Cheers!
    1
  1769. One pure strategy Nash equilibrium is for both players to hunt a stag with certainty. The other is for both players to hunt a hare with certainty. In either case, no one is mixing. Thus, they are PSNE and not MSNE.
    1
  1770. I'm not sure what exactly you don't understand. Could you be more specific? The two PSNE are equilibria for the reason explained in the video. The MSNE (which is 1/2, 1/2 and not 2/3,1/3) is a MSNE by virtue of the mixed strategy algorithm. So there are three equilibria. Game Theory 101 MOOC (#8): The Mixed Strategy Algorithm
    1
  1771. Equilibria in zero sum games are saddle points, so you might be observing something connected to that in how you worked on the problem.
    1
  1772. Thanks! And yes, the last five months have seen a lot of painful learning on my end on how exactly YouTube functions. Was that in just some random comments thread? I haven't heard of that subreddit before, and I couldn't quickly find where my work might have come up.
    1
  1773. Hey! It’s been a minute.
    1
  1774. Hi General 12th!
    1
  1775. Thank you!
    1
  1776. Thank you!
    1
  1777. But what if it's cats?
    1
  1778. That would work here because it is a zero sum game but would not generalize to no-zero sum games.
    1
  1779. Very kind of you, thanks!
    1
  1780. Questions about second-order consequences are my favorite thing to research. (Warning: I do this professionally with war. I am not an area expert on the U.S. financial system.) The FDIC, as the name suggests, only covers deposits. I'm not super knowledgeable about the details of the Robinhood problem, but it seems like that was outside of the FDIC's coverage. But your point is still important: insurance creates moral hazard. At least with the FDIC, though, there appear to be enough regulatory mechanisms in place that abusing the insurance would be really difficult (if perhaps still possible) in practice.
    1
  1781. That’s my voice 🤷🏻‍♂️
    1
  1782. Thank you!
    1
  1783. Okay, I will try in this way next video---though I have someone else suggesting it should be "Les linges sur les cartes"... Perhaps you two could reach a negotiated settlement and avoid the costs of war.
    1
  1784. Thank you, glad to hear! Please leave a revue when you are done. It really helps!
    1
  1785. Very generous, thank you!
    1
  1786. I believe you are correct.
    1
  1787. +Marissa J It's counterfactual thinking about what WOULD happen if had threatened instead of accepting at the start. This information is important because the quality of the outcome where he would declare war in the future determines whether he should threaten or accept at the start.
    1
  1788. Oh, wow, you're right. Tim Guldimann is Swiss. I've been getting this wrong for six months now. Yikes.
    1
  1789. In the model in my paper, the U.S. has a high war cost early in the game that slowly decreases over time.
    1
  1790. Thank you!
    1
  1791. Thank you!
    1
  1792. No, thank you!
    1
  1793. Yes! Hopefully later in the summer.
    1
  1794. Thanks! I actually ad-libbed the Percy Cox one. :D
    1
  1795. Yep!
    1
  1796. Wow, just noticed that. The photo is directly from the Ayatollah's official website. I can only speculate someone retouched the photo poorly.
    1
  1797. Thank you!
    1
  1798. @porgy29 I thought risk aversity had something to do with this at first, but that ends up not being the case. I'm covering risk aversity later and the extension should be pretty easy to see. Some people interpret this as people are loss averse, which dips into prospect theory, but I am not sold.
    1
  1799. No, thank you!
    1
  1800. Thank you!
    1
  1801. Gerne geschehen!
    1
  1802. I think the latter is the more likely explanation. Whatever Putin's speech is about in the next few hours will likely be what I do my next video on.
    1
  1803. Thank you again!
    1
  1804. Thank you very much!
    1
  1805. Any time!
    1
  1806. Third!
    1
  1807. boop (certified first comment)
    1
  1808. Selv tak!
    1
  1809. Very generous, thank you so much!
    1
  1810. Material is not materiel! https://en.m.wikipedia.org/wiki/Materiel
    1
  1811. The 2022 Winter Games were in Beijing!
    1
  1812. Wow, you actually were the first on two of them!
    1
  1813. @philnoll There are arbitrarily many equilibria. To see this, let's impose the rule that if there is one pirate remaining, he receives everything by default. If there are only two remaining, the second ranked pirate receives everything by default, and the captain survives because he votes yes. When there are three left, the captain can give the second ranked pirate any positive amount of gold. This induces #2 to accept and thus keeps the captain alive.
    1
  1814. Not much. The aid isn't necessary to authorize the weapons, and someone else could quickly replace the aid to actually carry the football.
    1
  1815. There's a long list of successors: https://en.wikipedia.org/wiki/United_States_presidential_line_of_succession#Current_order_of_succession
    1
  1816. Succession goes to the Speaker of the House, and presumably the military would have some sort of contingency plan to give the Speaker access to the weapons in a timely manner. It's worth keeping in mind that the football does not contain a "button" to fire the weapons. They are just codes.
    1
  1817. You probably wouldn't be able to do much: https://www.youtube.com/watch?v=zf5143Wq96E
    1
  1818. Yeah I am on it. The political scientists moved there about a year ago. Tag is @gametheory101
    1
  1819. There’s a notification bell so you get pinged immediately upon upload!
    1
  1820. Definitely added after original animations were completed
    1
  1821. Thank you!
    1
  1822. Thank you!
    1
  1823. Ah, okay. If you leave two full columns intact, you will lose. The video linked covers that subgame (using rows instead of columns, but it's all the same). If you leave me two full columns, I can take just the single corner piece on my turn. From there, no matter what you do, I can always leave the columns such that the right column has one fewer piece than the left. This eventually means we will get down to a situation where I leave just the poisoned corner, thereby forcing you to eat it.
    1
  1824. It sounds like you are right about how to win when there are only two columns left. See here: https://youtu.be/lmiPhe5zkk8 The problem with implementing that as the winning strategy for a generalized rectangle is that you need to have exactly one more piece in the right column than the left column at the end of your turn. However, the rules of the game dictate that you must eat everything above and to the right of the square you choose, so it is not possible to make that configuration.
    1
  1825. Well, you did subscribe, so two out of three ain't bad.
    1
  1826. I dunno, it’s the mid game at this point. Ancestral Recalls or Time Walks might be better.
    1
  1827. Thank you, that's very kind!
    1
  1828. Putin can afford the duals!
    1
  1829. Gracias primo
    1
  1830. It’s a U.S. test: https://en.m.wikipedia.org/wiki/Desert_Rock_exercises
    1
  1831. Thank you!
    1
  1832. @lateralexrex You would get more risk acceptance. A basic utility function of a risk averse person would confirm that.
    1
  1833. @TS114 The cost is free, but I don't think you understand. You would rather take a 50/50 shot between $0 and $1 million versus me just handing you $999,999?
    1
  1834. @lazarra101 I think the war literature is the most interesting. Search for "Rationalist Explanations for War" by James Fearon (1995 International Organization).
    1
  1835. Yeah, I never made it that far. Sorry. x^a, where a > 1, is the normal risk acceptant utility function. x^a, where 0 < a < 1, is the normal risk averse utility function.
    1
  1836. I'm just outlining at the moment. I might start writing over the winter break. I want to have 101 game theory puzzles ("Game Theory 101's 101 Game Theory Puzzles"). If I did one a day, then it's possible that the project will be fully wrapped up by July.
    1
  1837. I haven't seen this in models of uncertainty, but there are a bunch of cases with commitment problems where the state that would have a war initiated against it is better off by raising its own costs. This resolves the commitment problem and convinces its opponent not to fight, which makes everyone better off.
    1
  1838. I just gave generally agreed upon necessary conditions, not sufficient conditions. The Boston marathon bombings have all three of those qualities but I would not call it a terrorist attack. Others would disagree with me. Hence the problem.
    1
  1839. Does insurgency count? I was thinking Cuba pre-Castro or China pre-Mao.
    1
  1840. Done! Different but improved playlist: https://www.youtube.com/watch?v=ZZQ3wc92a_s&t=0s&index=9&list=PLKI1h_nAkaQq44yiYz_5eNByopc_D_U-G
    1
  1841. Thank you!
    1
  1842. Thank you!
    1
  1843. You have to guess and check as you go.
    1
  1844. Semi-separating equilibrium is three videos away. But I have no schedule for it, and the semester is about to start. So it could be anywhere from three weeks to six months before I get around to doing it.
    1
  1845. It is indeed wrong!
    1
  1846. @TheOneBlackSheep1973 Well that's a non-sequitur.
    1
  1847. @TheJoK3RHD Yes, it is from him.
    1
  1848. @ghosty121212 Undergrad was UC San Diego and grad school is University of Rochester.
    1
  1849. @Xavygravy Yes, it is called "weak dominance."
    1
  1850. @SonOfNye I have no idea, I am a political science PhD student.
    1
  1851. @DJTripleThreat78 I could, but not now. That logic uses Bayes' rule, which comes up in incomplete information games...but I'm still a long way off before I start doing incomplete information stuff on YouTube.
    1
  1852. @MPearce686 search: game theory 101 subgame perfect or go to my website
    1
  1853. Who is Dawkins? I don't understand. (Sounds British, though.)
    1
  1854. @Andreas0424 You right that can get cooperation if you play this game repeatedly (and indefinitely), but there is no precedent to set in the one-shot version of the game (like the one in the video).
    1
  1855. @athinggoinon Confess is a strictly dominANT strategy, not a strictly dominATED strategy.
    1
  1856. @Andreas0424 @Andreas0424 Nash didn't really come up with any of these games. The "stag hunt" seems to be what you are looking for, though.
    1
  1857. @AalsperZ Done. Thanks. Links are live.
    1
  1858. @Psycatalyst Links are live.
    1
  1859. Thank you!
    1
  1860. Thank you!
    1
  1861. Thank you!
    1
  1862. Kind of. I want to write a book on how Ukraine survived, so I am going to be using a handful of videos over the next few months to serve as an outline of the pivotal moments.
    1
  1863. Graag gedaan!
    1
  1864. Yep, it’s a Gnomes reference!
    1
  1865. Thank you!
    1
  1866. I think they are support trucks from the airport, but yep!
    1
  1867. 🤣
    1
  1868. @1337SuperNewb Bingo.
    1
  1869. That's correct.
    1
  1870. It won't. I don't know of anyone else who says that a full game is not considered a subgame, but the point is trivial.
    1
  1871. @Loosner202 No. That is a violation of 0:25. p must be between 0 and 1, not inclusive of 0 and 1.
    1
  1872. @Loosner202 But it could be .9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999.
    1
  1873. I won't! But that's okay.
    1
  1874. Thank you for the very kind donation!
    1
  1875. Graag gedaan!
    1
  1876. Incredibly generous, thank you!
    1
  1877. I see what you did there...
    1
  1878. Hmm, yeah, I see it.
    1
  1879. I see what you did there...
    1
  1880. I mean, in what world does someone HAVE to fire at someone? Life is not a video game with bizarre rules.
    1
  1881. Why is the first guy firing at anyone at all??? Baffled.
    1
  1882. Thank you!
    1
  1883. Thank you!
    1
  1884. Thank you!
    1
  1885. If the likelihood of selfishness is higher and there are fewer individuals, then the bad guy's plan does not always work.
    1
  1886. I don't remember that scene. Try YouTube searching for "game theory 101 volunteer's dilemma" and tell me if it remembers that situation.
    1
  1887. If anything, I would expect that the pressure of the situation would make people MORE likely to give up the information, not less.
    1
  1888. Here's an example: https://www.youtube.com/watch?v=WBCWwTGMNdc
    1
  1889. +Sami Samim Yes. Keep watching. There are some examples upcoming.
    1
  1890. No plans at this time.
    1
  1891. Sorry, but I got DS9 at #1!
    1
  1892. It’s in the video description. Sorry, don’t have the link easily available to copy/paste here.
    1
  1893. I wrote a blog post on how I make figures for my articles that might be helpful: https://williamspaniel.com/2020/08/10/how-to-make-figures-for-formal-articles/ You might also read through some of my papers, especially the more recent ones. I try to make sure there are figures for every important result in papers that I write now.
    1
  1894. It’s an honor and a privilege.
    1
  1895. +Tower1 Anything for you, King Wu.
    1
  1896. My bad homie
    1
  1897. Not sure.
    1
  1898. Already written, my friend.
    1
  1899. I’m actually the second from the left at 5:19
    1
  1900. The distance the Greek PM was from the blast has various conflicting reports, which is why I described it as less than a kilometer. I am not confident that 500 feet was the correct distance.
    1
  1901. @A2THEANDREW23 I don't do physics, but I think so. Is this similar to why a bouncy ball eventually stops bouncing?
    1
  1902. @1337SuperNewb He will if he can take the steps fast enough--think of a bouncy ball falling to the ground. Is this possible? Well, have you seen Shawshank Redemption? If Tim Robbins can do that, he can do anything.
    1
  1903. It's more strategic and less about intuition. We ultimately want to solve for S but there are a whole bunch of terms making things inconvenient. Creating the second line and subtracting it from the first is just a tricky way of removing a whole bunch of terms that would otherwise muck things up.
    1
  1904. Try watching these two videos. They are how I teach them in an actual class. The only difference is that the class teaches it in one dimension, but the idea is the same in two dimensions. https://www.youtube.com/watch?v=7b016FHOPsI&list=PLB5965C13F4B0B2DA&index=17 https://www.youtube.com/watch?v=KeNg1k0y8OA&list=PLB5965C13F4B0B2DA&index=18
    1
  1905. Welcome!
    1
  1906. Thank you!
    1
  1907. That's Moscow
    1
  1908. Try what I've sent to your inbox. YouTube doesn't like links being posted in the comment space. :(
    1
  1909. @ShahrozS Sure. Search "game theory how to deal with the police" on YouTube, for example.
    1
  1910. Thank you! Please leave a review when you are done. It really helps out.
    1
  1911. @blurfldyick Oops, you are right. The derivative will remain 0, though, so the conclusion reached is still correct.
    1
  1912. Thank you!
    1
  1913. Thank you! That was very generous.
    1
  1914. Thank you!
    1
  1915. Next week is a lines on maps fest…
    1
  1916. Thank you!
    1
  1917. Thank you!
    1
  1918. Thank you!
    1
  1919. I don’t!
    1
  1920. The translations Google produces (or even a professional translator) are not the official words coming from the Kremlin. The parts of the website that the Kremlin does translate are official.
    1
  1921. Actually, I'm thinking of turning this video into a fundraiser to build a parking garage.
    1
  1922. @DJTripleThreat78 Well, the next lecture in this lesson is already up, though it's a repeat from the bargaining games playlist....
    1
  1923. @DJTripleThreat78 If you already understand what's going on with Rubinstein, then you don't really need the next one on the playlist. You can wait until I get around to putting the next video up. :)
    1
  1924. @1337SuperNewb That's what I get for copying and pasting! Fixed with annotations. Good catch, my bad.
    1
  1925. Thanks!
    1
  1926. @MarkProffitt This assumes that players make moves randomly, which isn't sensible for the purposes of backward induction (unless a subgame involves a MSNE, which is not the case here).
    1
  1927. @fire17102 A vote up from me. I'd offer more, except I am a broke graduate student.
    1
  1928. Billy Heanue You'd definitely want to if you could, but you might imagine that you won't be able to cross the island in time.
    1
  1929. Thank you!
    1
  1930. The short videos aren't going away. But new research gets conference-style presentations.
    1
  1931. Correct on both accounts. I think I laid out the rules for the payoff function in the last video: more cookies are better for less, and you only care about what the other one gets given you have secured your own payoff. (That is, if I get 5 cookies, I would prefer you get 0 to 1 to .2 to .. to 7.) How this works in experimental game theory is pretty interesting. Maybe I will get to that eventually.
    1
  1932. Once you have divided everything by V, the proposal is standardized to a quantity between 0 and 1. Setting V = 1 once V has been shifted into the cost term is double standardizing and completely erases the V quantity rather than suppressing notation by implicitly combining the c term with it. (I understand that this is confusing, and typing away answers isn't the easiest way to communicate the thought process.)
    1
  1933. The reason for standardizing the value is to allow you to do this. Remember that the true cost terms are written as c/V, and V is how much an actor values the stakes. So if one party values the stakes much higher than the other, then that party is dividing their c quantities by a much larger number. The rest of the figure warps around that accordingly.
    1
  1934. My pleasure! Thank you so much for supporting the channel.
    1
  1935. Nice. Good luck. Tell your friend!
    1
  1936. You should just eliminate a strictly dominated strategy whenever you find one.
    1
  1937. One at a time!
    1
  1938. Where did the 5 come from?
    1
  1939. And by friend, I mean friends. =/
    1
  1940. The ability for the second player to switch the first move like that guarantees the that the second player wins for these types of games. (That is, games where players take turns, there is no private information, and no source of randomness.) So I would describe that rule as unfair, with the caveat that player 1 or player 2 can always force a win anyway, and that choosing who goes first also determines who wins.
    1
  1941. Watch the “12 Causes of the War” video. It is the basic guide.
    1
  1942. X is the percentage of the good that A keeps, so it's also between 0 and 1. (If p + cB is greater than 1, then A can only demand 1.)
    1
  1943. There's a set order for the playlist. It might help if you go to my channel and start at the beginning.
    1
  1944. But you can get whatever you would get out of war through bargaining (and perhaps more) AND still leave enough leftover to satisfy the other side as well.
    1
  1945. Even if you win the war, you still have to pay in terms of loss of life, compensating your soldiers, etc. The winner of the war derives a benefit (worth 1), but this cost is still present.
    1
  1946. Very kind, thank you!
    1
  1947. Sselv tak! That is very kind of you.
    1
  1948. No, thank you!
    1
  1949. Occupational hazard!
    1
  1950. No, thank YOU!
    1
  1951. Thanks for letting me know! I just fixed it.
    1
  1952. It's confusing because I showed the arrows going over land, but the travel is actually by sea. Hence Southeast Asia is closer than East Asia.
    1
  1953. It's from 2015!
    1
  1954. Short answer: Developing countries have higher rates of return (growth is easier when you can copy/paste from a successful formula) that can compensate for the risk in expectation.
    1
  1955. Very kind of you, thanks!
    1
  1956. Someone actually does this! I think it was in Manilla. I appreciate the kind words regardless.
    1
  1957. Nice catch! The State Department Flickr has a lot of nice public domain photos. I needed a picture of a Russian business, so I searched on there and found this, then did some research to see what Dunkin’s Russia policy was, and slightly rewrote the script to reflect that.
    1
  1958. I'm on a break for a month, then I'll start posting new material.
    1
  1959. Ross Leavitt No clue what he's talking about.
    1
  1960. You are amazing, thank you!
    1
  1961. Thank you for your generosity!
    1
  1962. Congressional voting districts circa 1946!
    1
  1963. If you pause at 2:35 and start plugging in values (make c_1 very high), you will see that the answer is no.
    1
  1964. Third, sorry!
    1
  1965. Thank you!
    1
  1966. +Cameron “Keith” Lowes This is the main playlist for the course: https://www.youtube.com/playlist?list=PLKI1h_nAkaQoDzI4xDIXzx6U2ergFmedo The most recent iteration doesn't go too deep into repeated games, however.
    1
  1967. In the series, there are eight or so of these goons, so it's safe for Hank (the police) to discount such a possibility.
    1
  1968. Well, yeah, basically everyone worldwide is stuck caring about U.S. politics. Maybe join me on the south pole of the moon?
    1
  1969. Thank you!
    1
  1970. Thank you, that's very kind!
    1
  1971. Thank you, that is generous!
    1
  1972. Thank you for your support!
    1
  1973. Thank you!
    1
  1974. Graag gedaan!
    1
  1975. Thank you! You know, I am going back through all my old comments, and I just noticed that you donated quite a bit. Sorry I didn’t thank you earlier for all of this!
    1
  1976. Thank you!
    1
  1977. Thank you!
    1
  1978. @DamionCrane My website has everything in order.
    1
  1979. Dunno.
    1
  1980. I cover that here, especially toward the end of the video: https://www.youtube.com/watch?v=0aAss6_e_W0&list=PLKI1h_nAkaQoDzI4xDIXzx6U2ergFmedo&
    1
  1981. @DubaiGuy08 Not quite. The probability distribution you gave--where 1 goes up 1/6th of the time and down 5/6ths of the time, and 2 goes left 1/3rd of the time and right 2/3rds of the time--is the MSNE. We don't actually know what will happen until the players make their moves, since they are moving randomly.
    1
  1982. @heath1444 I didn't know I sounded like Ed Norton, but I'll take it!
    1
  1983. @mrosendal Actually, there IS a strictly dominated strategy. But it is in mixed strategies. I will PM you a link.
    1
  1984. @mrosendal You learn matrix algebra or your head will explode. More on that in future videos.
    1
  1985. 1) Go to my channel and click on the playlist there. It's the newest, cleanest, and complete-est of the playlists, and there won't be anything wrong with it. 2) It depends on what you are studying and what your aims are. I study country-level behavior, so I don't have to worry about individual...umm...stupidity.
    1
  1986. @FilthParade Matching pennies is a zero-sum game, btw.
    1
  1987. Indeed! The picture is right, the script is wrong.
    1
  1988. Those are the percentage of ethnic Russians, not Russian speakers.
    1
  1989. Thank you!
    1
  1990. https://en.wikipedia.org/wiki/Materiel
    1
  1991. I couldn't! But there was a second, more subtle one that I weaved in here too...
    1
  1992. I have a couple of videos about poker on a different playlist: https://youtu.be/zKf45cHmJ0E https://youtu.be/N68s_UgOFBc If I can craft an interesting poker-based puzzle, I will definitely do one in this playlist's style. However, as of right now, I don't have any plans.
    1
  1993. Yeah, it’s pretty straightforward to implement, especially when each player only has two strategies. Google “Nash equilibrium calculator” or “ game theory calculator” and you will get a lot of options.
    1
  1994. "Who's the best free agent?" will be in tomorrow's poll!
    1
  1995. Do you, though? Ninjas are dying here!
    1
  1996. I have started one, and I am hoping to finish it over the summer.
    1
  1997. Thank you!
    1
  1998. Because materiel means military materials. It's not misspelled.
    1
  1999. I guess I snuck in there on a technicality. But I guess this is a deep question: if a video contains a screenshot of a video with lines on maps, does the original video have lines on maps?
    1
  2000. Thank you as always!
    1
  2001. You are welcome!
    1
  2002. Check on the right. :) It's a battle.
    1
  2003. Yep
    1
  2004. Yes. But also no. :)
    1
  2005. Thanks!
    1
  2006. @OnAFirefly I'm not sure which I like better or if I simply need both. =/
    1
  2007. It looks right. There are slight (but important) differences.
    1
  2008. @GelatinGhost If you flipped a coin, my best response would be to always go to my preferred form of entertainment. You can do some quick calculations to verify this.
    1
  2009. @mhretchin Yes, there is a lot of research on this.
    1
  2010. Those would all be payoff equivalent. If I play my new strategy, I am guaranteed an outcome of 0. If I mix 50/50 between heads and tails, then my expected outcome is also 0. (If you mix, I get 0 on average; if you play your new strategy, I always get 0.) So these are payoff equivalent, not dominant. That being said, if you let each player have a slight amount of risk aversion, then the new strategy becomes dominant.
    1
  2011. @gianpinna I take it back. It just means that the player won't use that mixed strategy in equilibrium. For what it is worth, I have never had to make such calculations when solving a game before, so you probably don't need to either.
    1
  2012. Thank you so much!
    1
  2013. Thank you!
    1
  2014. One more scheduled for Tuesday!
    1
  2015. I see what you did there.
    1
  2016. Unfortunately, you are right. Perhaps I will look into redoing this one.
    1
  2017. @brandeisjks It would be the same expression with capital letters. The actual value of this fraction will differ, of course, according to what all of those variables equal.
    1
  2018. Oh, I know. Putin is in the photo of you look close enough. The problem is that there aren’t very many free-use photos of people marching on the streets in Moscow. :)
    1
  2019. Easily a dozen!
    1
  2020. The last column reads that ~P v (P ^ Q) is true if and only if one of the following conditions is met: 1) P and Q are both true. 2) P is false but Q is true. 3) P and Q are both false.
    1
  2021. I had ChatGPT write an outro once. It was terrible and I openly mocked it.
    1
  2022. First one to get it! I was a little surprised it took so long given that he's on the move.
    1
  2023. That's not him, though I can see how the shape kinda looks like it!
    1
  2024. Annotated with correction, thanks.
    1
  2025. No.
    1
  2026. Yes indeed! Congrats on being the first.
    1
  2027. Check the top center of the image, just above the lone guy in a vest writing something down.
    1
  2028. That's not it! It's the very, very specific image of him with the binoculars.
    1
  2029. https://youtube.com/@LinesonMapsExtra
    1
  2030. https://www.youtube.com/@LinesonMapsExtra
    1
  2031. https://www.youtube.com/@LinesonMapsExtra
    1
  2032. https://www.youtube.com/@LinesonMapsExtra
    1
  2033. https://www.youtube.com/@LinesonMapsExtra
    1
  2034. https://www.youtube.com/@LinesonMapsExtra
    1
  2035. https://www.youtube.com/@LinesonMapsExtra
    1
  2036. Thank you!
    1
  2037. Oops...
    1
  2038. Thank you!
    1
  2039. Now that is a journey.
    1
  2040. Thank you!
    1
  2041. Certified first!
    1
  2042. Yeah, I don't know what to make of the polling results either! But that's kind of the point with entrapment. Not knowing makes the alliance patron more cautious than they would ideally want to be.
    1
  2043. I don't think it is an active problem now. The point was that it could be in the future---or something like it, not just Karelia, as these concerns are extremely common in all alliance relationships. Public polling on it has a sizable minority (but still a minority) of Finns with irredentist preferences without the backing of NATO. Overall, I don't think these problems will ultimately stop NATO and Finland from having a productive relationship. For more, Wikipedia has a useful page on this: https://en.wikipedia.org/wiki/Karelian_question
    1
  2044. https://www.youtube.com/@LinesonMapsExtra
    1
  2045. Nope, that is the original Blue Marble photo!
    1
  2046. https://www.youtube.com/@LinesonMapsExtra
    1
  2047. https://www.youtube.com/@LinesonMapsExtra
    1
  2048. https://www.youtube.com/@LinesonMapsExtra
    1
  2049. Thank you!
    1
  2050. https://www.youtube.com/@LinesonMapsExtra
    1
  2051. https://www.youtube.com/@LinesonMapsExtra
    1
  2052. https://www.youtube.com/@LinesonMapsExtra Also, nice.
    1
  2053. https://www.youtube.com/@LinesonMapsExtra
    1
  2054. https://www.youtube.com/@LinesonMapsExtra
    1
  2055. https://www.youtube.com/@LinesonMapsExtra
    1
  2056. https://www.youtube.com/@LinesonMapsExtra
    1
  2057. Yeah that will always be a puzzle for me.
    1
  2058. https://www.youtube.com/@LinesonMapsExtra
    1
  2059. https://www.youtube.com/@LinesonMapsExtra
    1
  2060. https://www.youtube.com/@LinesonMapsExtra
    1
  2061. https://www.youtube.com/@LinesonMapsExtra
    1
  2062. https://www.youtube.com/@LinesonMapsExtra
    1
  2063. Somesh Shahi To turn things around, I guess the better question is: why would PSNE inherently exclude MSNE?
    1
  2064. No, thank you!
    1
  2065. Based on the duration of this video and the word count of the script, I don’t think so. But I did fiddle with the microphone settings, so the audio should sound different from normal.
    1
  2066. Better or worse? I have been fiddling with my microphone settings.
    1
  2067. Thank you!
    1
  2068. Very kind, thank you!
    1
  2069. Hope I pronounced your home with at least 50% accuracy!
    1
  2070. That might be true for all we know!
    1
  2071. Well, I do a lot of the writing of these videos from the gym. Maybe it was on to something!
    1
  2072. That's actually Bruce Buffer. I'm guessing Justin Roberts took it from him?
    1
  2073. YouTube momentarily broke apparently, because I put second in response to another comment. Haha.
    1
  2074. Thank you!
    1
  2075. Hmm, not sure. When I pull it up, it shows as deliverable to London addresses. Maybe give it a week for the system to get updated? Or the digital edition is ready to go (and cheaper).
    1
  2076. Thank you!
    1
  2077. Well, I did manage to sneak in the phrase at the beginning of the final chapter!
    1
  2078. Thanks!
    1
  2079. @DJTripleThreat78 Like.
    1
  2080. @inthepants117 No?
    1
  2081. @DJTripleThreat78 The annoyingly stupid thing about prisoner's dilemmas is that they model a lot of things...but police and prison scenarios aren't among them. The counterpoint is that the reason you get shanked if you snitch is for criminal masterminds to guard against this exact problem. One way to get around the prisoner's dilemma is to have some sort of external enforcement mechanism (i.e. shanking) which switches the individual decision makers' preferences to favor cooperation.
    1
  2082. @JimBobJenkins So, basically, there is another level to the game, even though this matrix claims to present a prisoner's dilemma. It could be modeled fairly easily (and likely has been, many times) .
    1
  2083. @SilverscreenSurgeon This is not the case for the reason described precisely in the video. This issue comes up as a problem with backward induction in the centipede game, which I covered previously.
    1
  2084. @JimBobJenkins Well, off the top of my head, there's been: 1) the prisoner's dilemma. 2) the prisoner's dilemma again, because I didn't like the first one. 3) a general form of the prisoner's dilemma. 4) and now this one. There's going to be a bunch more on repeated prisoner's dilemmas, as it is pervasive in the literature. A bit basic, yes, but it has a lot of modeling characteristics that are useful for a variety of subjects.
    1
  2085. @DJTripleThreat78 For the sake of an introductory lesson, yes. But if you think that formal modelers sit around, stare at a prisoner's dilemma matrix all day, and randomly have new divine insight on international relations (as I once did), then you have it wrong (again, as I once did). The models get quite a bit more technical once you get deeper into the subject matter, but it's best to learn these things one step at a time, with the promise that we will respond to your reservations in time.
    1
  2086. Yes, but keep in mind that always defect for both players is also an equilibrium. (In fact, there are infinitely many equilibria in between, but the reason behind that is complicated.)
    1
  2087. @Vonzi0000 Never read it.
    1
  2088. @corporalcharlie Check gametheory101 then dot then com. (YouTube prevents posts that actually have the url.) I just launched it. Should have a lot of what you need.
    1
  2089. Thank you!
    1
  2090. Thank you so much!
    1
  2091. Thank you!
    1
  2092. Thank you so much!
    1
  2093. @silverspear08 Think of it like this: Player 2 gets to decide whether she wants to move center or right. Even if player 1 really likes it when player 2 moves in a certain direction, he cannot actually force her to play one strategy over another. So we only look at player 2's payoffs when we are considering whether any of 2's strategies are strictly dominated.
    1
  2094. @CAFowler2011 Nope. That's the great part about iterated elimination.
    1
  2095. If multiple outcomes remain after IESDS, you must look for Nash equilibria. See Lesson 1.4 of my textbook,
    1
  2096. Two suggestions: 1. Watch the more recent lecture series, which you can find on my main channel. 2. Buy the textbook. It's really cheap, has more examples, and goes at a slower pace.
    1
  2097. @abdihassanawali You to brute force the matrices until you find one that is strictly dominated. This can take a while. But once you find one, you can immediately eliminate it; if there are two or more that could be eliminated at the same time, there is no advantage or disadvantage to choosing one or the another first.
    1
  2098. @silverspear08 You can also go back to the prisoner's dilemma video if another game with the same property might help.
    1
  2099. @xBustx You should buy my textbook because it is cheap and I cover this. In the mean time, the answer is yes...and no. Search YouTube for "game theory 101 weak dominance" to get the explanation.
    1
  2100. @HomoForever This is a mechanical issue. The numbers represents the preferences over outcomes of the players, i.e. I prefer an outcome of 8 to an outcome of 6 to an outcome of 0, etc. So "8 is greater than 6" actually means "I prefer this '8' outcome to this '6' outcome." In turn, by definition, 8 is greater than 6.
    1
  2101. Correct. Recall that a best response is the strategy that generates the greatest payoff in response to all opposing strategies. A strictly dominated strategy cannot be a best response because there exists another strategy that pays more against ALL opposing combinations of strategies, including the specific one we care about.
    1
  2102. @Xavygravy 1) Something strategies cannot be eliminated at the start. You have to go sequentially before you can. 2) You could, but not for this game. If you really wanted to, you could just swap the numbers in the right column with the center column. 3) This is indeed wrong.
    1
  2103. @sanjog81 When searching for dominated strategies, you only look at the payoffs for the player whose moves you are looking at. Up and middle are player 1's moves, so we only look at the blue payoffs for the outcomes that follow from it. Middle may be bad for player 2, but she has no control over player 1 if he wants to play it. So up does not dominate middle. Also, [up, left] is clearly not an equilibrium because player 2 would want to deviate to middle and earn 4 points instead.
    1
  2104. I eliminated a column because it was a strictly dominated strategy. Whenever you find a strictly dominated strategy, you can eliminate it immediately.
    1
  2105. It won't matter who you start with. If you find a strictly dominated strategy, eliminate it immediately and see if the reduced game has more dominated strategies.
    1
  2106. Which square?
    1
  2107. @MrMirKuja Because we were looking at player 1's moves and therefore have to look at player 1's payoffs.
    1
  2108. The goal is to find strategies that individually optimal for both players given what everyone else is doing.
    1
  2109. @JimBobJenkins Most professors will teach this sort of mechanical stuff from the start. I don't because it is uninteresting, and students cannot appreciate the mechanical details until they understand the basics of game theory (even if the game theory is built off of these mechanics).
    1
  2110. @Son0fHobs Because of option A is better than option B in all cases, then you don't need to even consider option C to know that you should never play option B. Eventually, you have to consider option A versus option C (and that happens in this game), but you do not need to look at all three to see that option B is not a smart move.
    1
  2111. @MrMirKuja You eliminate rows based off of player 1's payoffs and columns based off of player 2's payoffs.
    1
  2112. Correct, there are usually multiple ways to get to the solution.
    1
  2113. +Rich Porter There are usually multiple ways to prove things. Here, though, it looks like you skipped the proper rearrangement of the sentences through association and commutation, so it doesn't check out fully.
    1
  2114. I don't know what that is.
    1
  2115. Wait, did you mean someone other than the golfer?
    1
  2116. That's chapter two.
    1
  2117. Yep, my mistake. Same problem around 4:50 as well.
    1
  2118. @niallsp The utilities are for the goalie and the sigmas (not thetas) are for the kicker. Both sigmas are for kicking left, so that should resolve the issue.
    1
  2119. You could do it that way too. For technical reasons, both are equivalent. I choose to keep it at 0 to better differentiate the players' payoffs.
    1
  2120. @billaudesvarennes This is saying that if both players know the kicker's stronger side, this is not a sensible strategy.
    1
  2121. @CogitoErgoCogitoSum The MSNE is not an arbitrary distribution as long as both of the negative numbers are the same, and it wouldn't be sensible to model it with different numbers. (That would be like I am more okay with giving up a goal to the right than I am to the left, which is...strange.)
    1
  2122. @niallsp I think it is like that in the video...no?
    1
  2123. Thank you!
    1
  2124. Thank you!
    1
  2125. Thank you!
    1
  2126. Thank you!
    1
  2127. That has a nice ring to it...
    1
  2128. Thank you! That is very generous.
    1
  2129. You have no idea how long I spent thinking "should I have the weeks start with Sunday or Monday?" knowing that whichever one I chose would backfire!
    1
  2130. Equilibria are strategies sets, not payoffs. So [middle, center] is the equilibrium; 3,3 is the payoff pair associated with that equilibrium.
    1
  2131. I don't hear it. But this literally the third YouTube comment that has said this, so what do I know?
    1
  2132. Yes.
    1
  2133. I sent page proofs to a printer today. So...if everything goes well...maybe there will be a paper book in a week? The printing cost is going to make the physical book considerably more expensive, though.
    1
  2134. It'd be a real Chad move...
    1
  2135. Oh no! Should have been "eastward" as the picture indicates.
    1
  2136. I get GTA vibes!
    1
  2137. Thank you!
    1
  2138. Here's a hint: think about what would happen if you did something irrational. What would this cause the other player to think about you? And how might that affect his decisions? There's actually a second problem with backward induction as a result of this game, but it isn't nearly as problematic as the one I am alluding to.
    1
  2139. @GelatinGhost Check the video on "problems with backward induction."
    1
  2140. I am redoing the entire series. Sorry to spam all of your subscriber inboxes.
    1
  2141. Glad it could help!
    1
  2142. The series predated the book by a couple of years. This is just the final version of the playlist.
    1
  2143. They promise fast treatment!
    1
  2144. This paper, among other things: https://williamspaniel.com/papers/nuclear/
    1
  2145. Nope, though it appears I was driving through Nebraska at about the same time as it. The nuclear fellowship ended last month.
    1
  2146. When I wrote that, I was assuming that I had already voted. If 1,500,000/1,499,999 is the result if I DON'T vote, you are correct.
    1
  2147. There is no budget constraint here. You value peace at $10 billion regardless of whatever happened previously.
    1
  2148. Yes! Maybe I will do a video specifically on the stability-instability paradox with what's happening there.
    1
  2149.  @benbernanke4037  Yep
    1
  2150. Yep, the game has imperfect information at player 2's move.
    1
  2151. Thanks for the toonie!
    1
  2152. The writer of this ^ comment is great
    1
  2153. No, I breathe too much into the microphone
    1
  2154. Econ or political science?
    1
  2155.  @anuragmukherjee1014  Player 1 never chooses threaten, so you wouldn't write it as an equilibrium strategy.
    1
  2156. Hey! Glad you like it.
    1
  2157. Very generous, thanks!
    1
  2158. Thanks big duke six
    1
  2159. Nailed it, congrats!
    1
  2160. !
    1
  2161.  @dandiculous Exactly. Even better than how I summarized it.
    1
  2162. Google News doesn’t provide clean numbers. 🤷🏻‍♂️
    1
  2163. Not sure what you mean. Where what failed?
    1
  2164. I can pledge to you that you will never hear me sing. I want people to enjoy their time on my videos, not cry in pain.
    1
  2165. That makes two of us.
    1
  2166. Thank you!
    1
  2167. https://youtu.be/pBwT-5z9R5A
    1
  2168. Yep, the "market for lemons" paper used that as its motivating example. It's also why a market for "lemons" is called that.
    1
  2169.  @Mercyreneeb  That ... that's even crazier.
    1
  2170. I appreciate the edit. :)
    1
  2171. "In case of nuclear winter, dress warmly."
    1
  2172. It’s “mistral”
    1
  2173. Yeah this would be a baffling channel for someone to stumble upon. The only coherent narrative is "things William Spaniel sometimes does for research purposes".
    1
  2174. +oglop In defense of the system, it's worth noting that I myself am "at the (a) university," so at least some of us are clear lecturers.
    1
  2175. @crescine They are just words to represent strategies. They could be "C" or "D" if that would help you. (But these terms are prevalent in the literature, so this comes at a cost.)
    1
  2176. @gowiemeister Nope--that sounds right.
    1
  2177. @damthatriver09 You are making your moves based off of how you think your opponent will play. (Here, the solution is simple, as defection is strictly better for you than cooperation.)
    1
  2178. @GodlessInfinity Game theory is not constrained by 2x2 matrices. It goes far beyond this.
    1
  2179. @Talusjay Good for you for taking interest.
    1
  2180. The first point is accurate, the second is not. The only assumption made about preferences is that the criminals only want to minimize jail time. They can have any preference for risk as long as they like less jail time than more time. Pre-mediation does not change these results for the the reasons outline in the video. Even if we "agreed" to keep quiet beforehand, I would still want to rat you out once the game actually began.
    1
  2181. @SecondStageConsult You are right that this is confusing, but those terms are prevalent in the literature. Might as well get used to them now.
    1
  2182. @Tarantula33222 Most games (or at least the interesting ones) have underlying mechanics that look like what we study. Search "game theory penalty kicks" for an example. Or "game theory baseball" for something a little more abstract.
    1
  2183. @SEBASTIANAG89 You're welcome...just spread the word!
    1
  2184. @Lisl07 A lot. Check Wikipedia.
    1
  2185. @YourACherrynut Isn't that the socially optimal result, though?
    1
  2186. Because they could always pick the strictly dominANT strategy and do better.
    1
  2187. @WITreasure If you are taking game theory, keep in mind that I have lectures that will take you all the way up to incomplete information.
    1
  2188. @yisoonshin12 No, the moves are simultaneous.
    1
  2189. @yisoonshin12 No sarcasm. Matrix games like this are simultaneous move games. If one could "see" what the other is doing, then you would be looking at an extensive form game. There is a separate lecture series for that. Check out my website.
    1
  2190. @billypk2 Because both players would switch to defect if they knew the other one is cooperating.
    1
  2191. @Joefest99 Cooperating means keeping quiet; defecting means ratting out the other.
    1
  2192. @cciccone61 Game theory describes strategic interactions between two more players. That example only has one player (the defendant), so you can't model it in the way I do here.
    1
  2193. @gotchacervix There are a lot of negative externalities associated with that. For example, you're wife will be a bitch--literally.
    1
  2194. Who'd have known that moody cows have good observation skills? Congrats on being the first!
    1
  2195. GPT-3. This video was recorded more than a week ago, before 4 became public. I might try again.
    1
  2196. Thank you!
    1
  2197. Just posted about it. That's amazing! Thanks for letting me know.
    1
  2198. Thank you for noticing! I re-rendered the entire video to add that after I had already uploaded the video.
    1
  2199. Whoops!
    1
  2200. Very generous, thank you!
    1
  2201. Thank you!
    1
  2202. Thank you!
    1
  2203. I noticed you've asked me this like four times, so you deserve an answer: I have no plans to do so, sorry. It would be very time consuming, and YouTube provides better returns.
    1
  2204. Thank you!
    1
  2205. Thank you!
    1
  2206. No, thank you!
    1
  2207. That’s super generous, thank you!
    1
  2208. It's like you are reading my mind or something.
    1
  2209. Did you seriously just make this comment? Did you watch today's episode? Holy hell, that woman blew it. I have the slides to film but I need to wait a couple weeks before I can get back to my recording equipment.
    1
  2210. There’s no math in the new one!
    1
  2211. Now that Bronnie is cleared to play, only good things.
    1
  2212. That got a literal lol out of me
    1
  2213. hi there hello
    1
  2214. LOM NFT, naturally.
    1
  2215. That is this playlist: https://www.youtube.com/playlist?list=PLKI1h_nAkaQrvKPtuPMXkU4yXCDSp_NHh
    1
  2216. Hi there hello
    1
  2217. Thank you!
    1
  2218. Yeah, I actually struggled with which words to use when I was writing that line. The tradeoff between conciseness and precision is always a challenge when covering technical stuff.
    1
  2219. Thank you!
    1
  2220. Gotta settle for flags on maps this time.
    1
  2221. I actually said it that way on the first take. If it weren’t for the turkey thing, the outtake would have been the end of the video!
    1
  2222. Thank you!
    1
  2223. Thank you!
    1
  2224. It would have been disaster in November. 😉
    1
  2225. @Papierumtg Rational choice's predictions are only as good as its inputs. So, indeed, purely analyzing games without taking a step back and making sure that the preferences and interaction make sense will produce some awful research.
    1
  2226. @datscilly Yup, thanks.
    1
  2227. @sehermerveakbas Outside of Arrow's rule (which deals with aggregated preferences, not individual preferences like we are doing here), I'm not aware of any systematic problems with transitivity.
    1
  2228. @sehermerveakbas I don't follow. Example?
    1
  2229. @agelao1 That keeps the rank ordering of the outcomes correct but not the preferences over lotteries of outcomes. For example, suppose I value outcome A worth 0, outcome B worth 1, and outcome C worth 2. I am indifferent between B with certainty and a coin flip between A and C. But try a cubic transformation. A is still worth 0, and B is still worth 1. C, however, is worth 8. Now I prefer the coin flip between A and C than taking B with certainty.
    1
  2230. That's the same question I have asked myself every time I encountered that articulation of the rules. It's not much better if one person is dictating the stakes. It's still a pure matching pennies guessing game.
    1
  2231. FWIW, I think the show is fine, but I am not sure why it has become a cultural phenomenon.
    1
  2232. This was my first super thanks ever received. Thank you so much! I will always remember it.
    1
  2233. Thank you so much!
    1
  2234. It's an error with the image. The phone call in question was on December 2, 2016.
    1
  2235. Ha!
    1
  2236. @ICarnag3I Do you mean a trual?
    1
  2237. @rockuser28 Watch again in the morning? If you have never seen a Nash equilibrium in your life, go to my website and watch the first few lessons? Buy my book and support my campaign for world domination? ;-)
    1
  2238. @nahaymath Expected utilities are scale-able (YouTube search "expected utility transformation"), so making the payoffs for Kitty's death a very negative value instead of zero is equivalent to making the cost parameter C very small. But no matter how small C is, as long as there is some cost, no one calls with positive probability.
    1
  2239. @Chiraliffy There will be a place for you in my rubber stamp parliament.
    1
  2240. @stuffedk Oh, and everyone has perfect aim in that formulation. I think it would be the same if some players could miss, though.
    1
  2241. @RamekoFX Yup, the story has grown more and more fictional through the decades. I talk about it in the book. That's also who I call the book a "parable," since the story is more parable than truth now.
    1
  2242. @stuffedk I know if you have a three player game and everyone takes turns, the first player should shoot his bullet into the ground. The second player then shoots the third player since the first player is of no threat, and so only the third player dies.
    1
  2243. @rockuser28 It's just an assumption here. There were about 40 people who witnessed the murder, some of whom yelled at the attacker to get away. This is also the simplest form of the game. I do an n-person one in the book.
    1
  2244. Artifact of my animation. I didn’t notice it until after the video rendered and I decided to just leave it because this is a breaking news event.
    1
  2245. +Jagvir Ji (Q ^ ~Q) is a contradiction, which allows us to conclude that the assumption for the proof by contradiction is false. Since ~P was the assumption for the proof by contradiction, we are left with ~~P (or just P).
    1
  2246. +Mr Syed Just eyeballing that, my recommendation is: https://www.youtube.com/watch?v=qzEk3UzCfVo
    1
  2247. The Rubinstein model has a bunch of important differences. I didn't discuss these in the video because they are boring, but I talk briefly about them in the actual paper. In the traditional framework, bargaining gets resolved fairly quickly because delay is costly to both parties. Sports contract extensions do not share this feature. Delay only becomes costly when the player remains unsigned going into the season. So, this paper asks whether something else can get negotiations going.
    1
  2248. (The answer is yes.)
    1
  2249. who cried a river and drowned the whole world?
    1
  2250. Thank you!
    1
  2251. Leftover!
    1
  2252. Yes, and Didi is Tommy's mother in the series as well.
    1
  2253. By the rules of the game, Tommy is constrained to only making non-negative offers. So, in short, no.
    1
  2254. They are analogous, which helps me keep them straight.
    1
  2255. It's just PowerPoint. Numbers only get multiplied by probabilities. In this case, that's Nature's move.
    1
  2256. @Mariopartyrules That is not the case.
    1
  2257. @OnAFirefly You could do this, but the result would be the same...and I don't run out of space on my slides my way. =P
    1
  2258. @SalinasNightmare I'm TAing for intro to international relations this semester. You can find my course page by Googling "William Spaniel IR 106."
    1
  2259. I grew up in a desert, so I think I am covered there. :)
    1
  2260. I lived in Rochester for five years, so I'm mostly indifferent at this point. More worried about how few sunny days Pittsburgh has every year.
    1
  2261. Haven't gotten to that yet.
    1
  2262. Thank you!
    1
  2263. The joys of stock photos…
    1
  2264. This is a YouTube-wide problem that I also have sometimes, both for my own work and other videos. Switching from native speakers to earphones (or vice versa) often solves it for me.
    1
  2265. Thanks! Hope you enjoy it.
    1
  2266. Nice!
    1
  2267. Thank you!
    1
  2268. Ironically, first!
    1
  2269. Graag gedaan!
    1
  2270. Very kind, thank you!
    1
  2271. Thank you!
    1
  2272. whistle podu
    1
  2273. The whole Russia/Ukraine thing probably won't be coded as a full war, but it's a notable recent case.
    1
  2274. I UNDERSTAND THE REFERENCE
    1
  2275. Physical copies are out!
    1
  2276. Yep, that definitely sounds like what I would recommend!
    1
  2277. Which one was that?
    1
  2278. Physical copies are out now!
    1
  2279. Thanks! Should only be a couple more days.
    1
  2280. I'm an American academic. I have my preference on who I want to see win the war, but I am also here to provide good analysis of what is actually happening, regardless of what I want to happen.
    1
  2281. Thanks!
    1
  2282. I guess that depends on your definition of detail. I have a few pages on it and Ukraine's decision not to develop nuclear weapons following independence.
    1
  2283. Thank you!
    1
  2284. Thank you!
    1
  2285. Thanks again!
    1
  2286. Thank you!
    1
  2287. @11cookeaw1 It has a mixed strategy Nash equilibrium. The game is called "matching pennies."
    1
  2288. Not randomizing between two or more strategies. "I will always play stag" is a pure strategy. "I will flip a coin. On heads, I will play stag; on tails, I will play hare" is not.
    1
  2289. @WhyYouStealMyName Nope. If the other guy plays rabbit/hare, your rabbit/hare is better than stag for you.
    1
  2290. @ForestGumpsFury You could think of the stag as worth six units of meat, and the hunters will split it equally, perhaps because 3 units is the most a single hunter can carry.
    1
  2291. @Dipesh101 Then you watch the next video. =)
    1
  2292. @thecapone45 No, but unfortunately I can't think of any videos that have a counter example off the top of my head.
    1
  2293. There is no generally accepted theory of equilibrium selection. So...there is no good answer.
    1
  2294. It could mean that. But really it is just saying that it is the best outcome for all parties.
    1
  2295. Yes, any outcome which is each individual's most preferred outcome is always coalition proof.
    1
  2296. Just imagine it's worth 6 units divided in two ways.
    1
  2297. Kind of right. In either of those cases, one is already playing stag. So in each case, ONE player would like to deviate.
    1
  2298. TheAntiParadox No. Battle of the Sexes is proof by counterexample: https://www.youtube.com/watch?v=2BdBWmL8tJc "Equilibrium" only refers to stability in strategy choices, not balance in payoffs.
    1
  2299. Miracles can happen!
    1
  2300. I talk about that in the book. It's okay if you leave both triple letter/triple word corridors open afterward. If you do, the sequence looks like this: 1) You play the double word/double word corridor. 2) Your opponent plays on a triple letter/triple word corridor. 3) You play on the other triple letter/triple word corridor. Net gain for you,
    1
  2301. It became a political argument, most of it in bad faith. This is a political science channel, and I try to keep it that way. The whole thing made me sad too. If you are curious about what I think about the Karelia situation, I wrote this in another thread: "I don't think it is an active problem now. The point was that it could be in the future---or something like it, not just Karelia, as these concerns are extremely common in all alliance relationships. Public polling on it has a sizable minority (but still a minority) of Finns with irredentist preferences without the backing of NATO. Overall, I don't think these problems will ultimately stop NATO and Finland from having a productive relationship."
    1
  2302. My bad!
    1
  2303. @gianpinna No, I've done virtually nothing with incomplete information.
    1
  2304. @gianpinna That's not going to be fun at all. What's the setup?
    1
  2305. @gianpinna Check your inbox.
    1
  2306. @edinhenrik I study international relations, so the classic example here is states doing worthless military exercises. They cost a ton but don't really do much for the actual quality of your military.
    1
  2307. Other than the occasional crossover, no. Not really.
    1
  2308. We can't give policy advice without first understanding the mechanisms driving war. (To do so we be like the blind leading the blind.) This is an introductory class, so these lectures are only skimming the surface. Plenty of classes are geared directly toward policy implications.
    1
  2309. https://youtu.be/Y74I4lJ7aWk
    1
  2310. You can always use the YouTube controls to turn up the speed to 1.25x or 1.5x! I do this for a lot of the videos I watch.
    1
  2311. This is the canonical work on that subject: https://www.hup.harvard.edu/catalog.php?isbn=9780674707580
    1
  2312. Thanks!
    1
  2313. None of this is AI.
    1
  2314. Thank you!
    1
  2315. =)
    1
  2316. France vs. Germany wouldn't count here since that is an interstate war. I should have also mentioned in the lecture that there were ~125 civil wars during that time period but only ~25 interstate wars, meaning that civil wars are far more prevalent.
    1
  2317. @nahaymath Sentential logic is a building block that eventually allows us to work on these types of theories. In fact, it's the first thing you learn at where I go to grad school.
    1
  2318. "But then, umm, we decided that we didn't want to use coal anymore..."
    1
  2319. It is for the period of nuclear coverage, and I try to have period-accurate flags wherever possible. https://en.wikipedia.org/wiki/Flag_of_Spain#Spanish_State
    1
  2320. OTAN is the French acronym for the alliance.
    1
  2321. > Wouldn't it make more sense to ditch the first company if they won't at least match the pay? That's why you would reject offers less than $20. > Why would he try bargaining if he could just accept the other company's superior offer? Why wouldn't you bargain with your current company if you know they are willing to pay you more than $20 and you have a credible threat to leave if they don't? And why wouldn't the company pay you more in that case?
    1
  2322. On the chart, the company is unwilling to pay $50 but is willing to pay anything less than that--including values between $20 and $50.
    1
  2323. That's the point. The original company should offer him enough to keep him around, since they value his work worth $50 per hour.
    1
  2324. What time? Maybe I misspoke.
    1
  2325. Yeah, it seemed like there was a simple misunderstanding going on.
    1
  2326. Is ABlinken, pronounced “Abe Lincoln”
    1
  2327. That is actually what happened. To be fair, though, his entire family was there.
    1
  2328. Started writing the back half in December.
    1
  2329. Thank you!
    1
  2330. Here’s a link: https://polisci.ucla.edu/sites/default/files/u245/andrew_bertoli_paper_05-01-17.pdf
    1
  2331. Watch to the end!
    1
  2332. p-value for the main result is 0.007
    1
  2333. Well, that is a superficially different deviation. But it turns out that the proof in the video covers it. If deviating in the second period is profitable, then it must be true that it pays more in total for the periods 2 to infinity than maintaining the grim trigger strategy. If you set up the calculation for this, you wind up with the exact same payoffs as in the video, except everything is multiplied by \delta.
    1
  2334. +supergreatsuper So there is some finite period by which the game MUST end, but the players don't know know in which period the game will end before that? That's a pretty straightforward model to solve if you have worked through the section on repeated games.
    1
  2335. +kikones34 Fixed, thanks.
    1
  2336. Thank you so much!
    1
  2337. Thank you so much!
    1
  2338. Thank you!
    1
  2339. Thank you, it's an honor!
    1
  2340. Thank you!
    1
  2341. Temple of Doom was released as a PG film; it was blowback in response to it that led to the creation of the PG-13 rating.
    1
  2342. I know what you meant, but the time stamp marks this as 90 seconds, which makes your comment seem like a savage diss. 😅
    1
  2343. Awesome, thank you!
    1
  2344. I always replace NSFL images with dogs. Those, in particular, were Obama's.
    1
  2345. Thank you so much!
    1
  2346. Thank you so much!
    1
  2347. Thank you!
    1
  2348. I appreciate your patience. A bunch of other commenters didn’t wait 20 seconds to complain! 😅
    1
  2349. Thank you so much!
    1
  2350. Gern geschehen! That was very generous of you.
    1
  2351. Thank you!
    1
  2352. Thank you so much!
    1
  2353. Why not both? 🤔
    1
  2354. That's an all-timer right there.
    1
  2355. Incredibly generous, thank you!
    1
  2356. Thank you!
    1
  2357. Shhhh don't tell anyone
    1
  2358. Thank you!
    1
  2359. Thank you!
    1
  2360. Happy birthday!
    1
  2361. Thank you!
    1
  2362. Thank you!
    1
  2363. Thank you!
    1
  2364. 100%. Game theory is just a complicated way to make sure arguments are valid, and learning to do it well has made my argumentation better even when there is no math involved.
    1
  2365. Gotta save the best part for the end.
    1
  2366. Thank you!
    1
  2367. Thank you!
    1
  2368. Yes indeed! And proof that I was in this for the long haul.
    1
  2369. No, thank you!
    1
  2370. Thank you!
    1
  2371. Ah, -40. A temperature we can all agree on!
    1
  2372. On break until January!
    1
  2373. !
    1
  2374. Thank you!
    1
  2375. Thanks! I will look into it.
    1
  2376. What do you think of the audio after 12:26? I did that part after the rest, and it was recorded differently. I changed my setup a few weeks ago and still haven't been satisfied with anything yet. (Except, perhaps, the post 12:26 version.)
    1
  2377. Alex Fredes Salas I am a political scientist, so I can't be of much help there. Sorry.
    1
  2378. If I knew the answer, I'd go with C F K U. After they'd make me re-shoot it, I'd switch to J Q Z U. Y M C A definitely has an advantage in that you can make something sensible and still keep the vowel tacked on at the end.
    1
  2379. https://www.youtube.com/watch?v=UaGM8T4o9xI https://www.youtube.com/watch?v=Zbr0c5QCpos
    1
  2380. Glad it was helpful!
    1
  2381. That's a really cool idea!
    1
  2382. No worries! I also kinda roll my eyes every time I have to record the same thing every week.
    1
  2383. They actually did! Here's the full quote: "On June 30, the Russian Armed Forces made a gesture of goodwill and completed the tasks on Zmiinyi Island and withdrew the garrison that was there." https://www.washingtonpost.com/world/2022/06/30/russia-withdraw-snake-island-ukraine-war/
    1
  2384. That's the trillion dollar question that only Putin's inner circle actually knows the answer to. :)
    1
  2385. @LaBambathereal We cover that. Search "game theory 101 rubinstein bargaining". Rubinstein bargaining has some very intuitive assumptions but removes any evaluation of "fairness," and you get the 50-50 split as you might expect.
    1
  2386. It appears I have inadvertently unleashed my perspective of laboratory experiments.
    1
  2387. @ForbiddianSC Those are some odd preferences.
    1
  2388. Game Theory 101: The Ultimatum Game
    1
  2389. They are mostly worthless. You have to get out of jail if you've failed to roll doubles the first two times, so using it saves you $50 on the third time. But you are right about jail being good. That's why I referred to the orange properties as being particularly valuable in the video--they are 6, 8, and 9 spaces away from jail, making them among the most frequently landed on spaces in the game.
    1
  2390. It's just a powerpoint!
    1
  2391. Thank you!
    1
  2392. Ah, I see. There is a slightly longer description of the intel run in that video, but nothing expansive.
    1
  2393. Thank you!
    1
  2394. Sometimes YouTube's encoding gets wonky. Sorry!
    1
  2395. I wanted to respond to this by saying “What a silly point.” But then anyone without a deep understanding of cricket fielding positions would think I was just mocking you. 😅
    1
  2396. @rung3000 I suppose it (unintentionally) kind of is.
    1
  2397. Player 1 has four strategies: (Go, Agree) (Go, Disagree) (Stay, Agree) and (Stay, Disagree). That gives you a 4x2 matrix, and you can fill in the payoffs by taking the strategies for any given cell and following them through the path of the game tree until you reach some terminal payoffs.
    1
  2398. Pure strategies are mixed strategies--you mix with probability 1 on one strategy and probability 0 on other strategies. You won't ever hear anyone mention this outside of Nash's theorem, though.
    1
  2399. Yep!
    1
  2400. 17 references by 65 minutes by my count
    1
  2401. Thank you!
    1
  2402. There’s one from episode nine and one from Mando, but the rest are the first six.
    1
  2403. https://en.wikipedia.org/wiki/Cornhole
    1
  2404. I am now disappointed in myself.
    1
  2405. Nah. It’s been a month.
    1
  2406. Thank you!
    1
  2407. Any time!🙃
    1
  2408. Thank you!
    1
  2409. @ghosty121212 Sadly, I just began grad school, so that's at least ten years away.
    1
  2410. @Crissix100 It's absolutely meaningless. If YouTube allowed me to change it, I would jump at the chance.
    1
  2411. Somewhat! But the "banks don't have a pile of money in the back" has an analogous version of "banks don't have a lot of 000s sitting idle on their computer servers." The prevalence of digital money is helpful for deposit insurance because you don't actually need a bunch of armored vehicles dropping off bags of cash. You just need someone in a central bank to press a few buttons on a computer. But when things get really, really bad, people are still going to want to have physical cash, so button pressing can't solve all the problems.
    1
  2412. I’m still regretting not putting in a “lines at banks” joke.
    1
  2413. Guess you will just have to settle for the temporary channel logo. ¯\_(ツ)_/¯
    1
  2414. Looks like it’s the crypto bots that are moving in…
    1
  2415. Nope, never been to Penn State. There is a good chance if you have ever gotten game theory help on YouTube that I was the disembodied voice.
    1
  2416. That is correct. But remember that pure strategies are mixed strategies.
    1
  2417. The best kind of student!
    1
  2418. Be that as it may, still incredibly generous!
    1
  2419. You got me for a second that this was a real comment…
    1
  2420. The easiest way to remember what's going on is to look at the v at the end of the line and think of it as a greater than sign. If A -> B, A > B.
    1
  2421. Thank you!
    1
  2422. Thank you!
    1
  2423. Thank you! That was very generous.
    1
  2424. Oops, sorry. Good catch.
    1
  2425. Elijah Lee The next lecture covers all possible cases.
    1
  2426. Good thing you weren't playing Jund. =)
    1
  2427. Check 5:01!
    1
  2428. The algorithm controls is all.
    1
  2429. Didn’t notice this until now!
    1
  2430. Is it in Europe? 🤔
    1
  2431. As the producer of this content, I somehow find myself in agreement here.
    1
  2432. Well, if the strategy works, Russia will be deterred, there won’t be a further conflict, and thinks in Slovakia will be pretty awesome!
    1
  2433. Thanks!
    1
  2434. Awesome, thank you!
    1
  2435. Evergreen comment on all of my videos. 😆
    1
  2436. Just your basic PowerPoint.
    1
  2437. I didn't know you could get reception for YouTube while hiding under a box.
    1
  2438. @artanis00 I suppose it is because they can't get over there in time.
    1
  2439. It’s me
    1
  2440. +Syed Ameed The antecedent does not need to be a simple sentence. But single letters (like F) must be simple sentences. "I do not pay fees" = F isn't good because "I do not pay fees" is not a simple sentence. "I pay fees" is, however. So that's why we have ~F in the example.
    1
  2441. When you hit lecture 18 (contraposition), you will see that ~H => ~V is identical to V => H!
    1
  2442. Daniel Mckissick Jr If you are asking whether p => q is the same as q => p, the answer is no.
    1
  2443. Because you might have to pay bank fees for reasons other than not having a $1,000 balance.
    1
  2444. 5:25
    1
  2445. Thank you so much!
    1
  2446. Yes master
    1
  2447. Thanks. I did that one on the fly!
    1
  2448. @OnAFirefly No. We sat there. It took forever. He kept asking me if I wanted to change my mind. I kept saying no.
    1
  2449. @DJTripleThreat78 That would be the NE (Norris equilibrium).
    1
  2450. @affablegiraffable Disagree!
    1
  2451. @DeJach You are right. In retrospect, I should have pushed this a little more. It is questionable if he could hold me for that long while we waited for the dogs.
    1
  2452. Indeed, that's an important assumption.
    1
  2453. To be clear, you can talk about it all you like. But the meaning of "it" is unclear due to the paradox.
    1
  2454. No. You could restrict it further to the class of finite games as well.
    1
  2455. @affablegiraffable I have been for about eight months.
    1
  2456. That's mostly right. The stoplight game also has a MSNE which is Pareto-dominated, but I didn't cover it here/
    1
  2457. It's a bit under 300 pages. It will keep you busy. If you eventually want to become an "expert" on the subject, you are pretty much stuck buying the $75 textbook from Fudenberg and Tirole. But that's written more as a reference manual than an actual teaching book.
    1
  2458. Yes.
    1
  2459. Pure strategy Nash equilibrium is a subset of Nash equilibrium. When you get deeper, you learn of another type of Nash equilibrium known as mixed strategy Nash equilibrium. That shows up in my course here: https://www.youtube.com/watch?v=fvEQujUcPv4&list=PLKI1h_nAkaQoDzI4xDIXzx6U2ergFmedo&index=7
    1
  2460. @TinBryn I'd like to see you try!
    1
  2461. And I'm here in 2021 because the game theory gods won't let me leave. Help pls.
    1
  2462. Yes. Player 1 plays B and player 2 mixes between A and B.
    1
  2463. Thanks!
    1
  2464. If the other side faces a budget constraint, then yes.
    1
  2465. There are a few problem sets on the Udemy version of the course: https://www.udemy.com/gametheory101/
    1
  2466. What was the Reddit thread if I may ask?
    1
  2467. +duskcheetah I can't give a great answer given that we don't really have much data to go off of. What I did find out in my investigation is that about 70% of tickets sold are quick picks, so I'm not sure how much additional value a non-birthday ticket would have over a birthday ticket.
    1
  2468. Because both players earn strictly more by coordinating with certainty than what they earn by mixing.
    1
  2469. @Jefgg I'd rather talk about PRACTICE.
    1
  2470. @PeopleMakingSound You should go to my website to get the correct ordering.
    1
  2471. @Jefgg Allan Iverson in his second career?
    1
  2472. The link is in the annotation at the beginning of the lecture.
    1
  2473. +Oscar Walet Thanks!
    1
  2474. @Vonzi0000 Knowing what dominates what helps when you are finding mixed strategy Nash equilibrium. This isn't exactly obvious, and I haven't covered it yet, but finding MSNE is extremely time consuming in games larger than 2x2. Finding dominated strategies (even weakly dominated) saves a lot of time.
    1
  2475. Thank you!
    1
  2476. @blackrobe2007 I just did the math, but YouTube doesn't let it go in the comments. YouTube fail.
    1
  2477. @christophnguyen It's the same no matter how many rounds you play.
    1