耶鲁大学博弈论公开课 on Yagu的小站

耶鲁大学博弈论公开课 - 第1集导论-五个入门结论

Thu, 11 Jun 2026 00:30:00 +0800

视频信息

标题: 耶鲁大学博弈论公开课 - 第1集导论-五个入门结论
BV号: BV1u54y1k74g
分集: p1
时长: 68分34秒（4114秒）
作者/来源: 耶鲁大学公开课
原始链接: B站视频
转录方式: Groq Whisper 英文转录；英文在前，中文在后逐段对照。

视频摘要

本集是耶鲁大学博弈论公开课第 1 集，主题为“导论-五个入门结论”。课程以英文课堂讲授和互动讨论为主体，围绕课程定位与博弈论入门展开，逐步引入博弈论中关于策略、收益、信息、均衡和动态推理的分析框架。本文提供英文原文与中文译文逐段对照，便于跟读、检索和复习。

核心要点

课程定位与博弈论入门：本集围绕“导论-五个入门结论”展开，是理解后续博弈论模型和课堂案例的基础。
战略环境与收益目标：讲授重点放在参与者如何根据目标、信息和他人行为选择策略。
严格劣势策略：课堂通过案例、提问或推导展示抽象模型如何落到具体决策情境。
课堂实验与五个入门结论：内容强调从结果反推策略条件，训练形式化的战略思维。

点击展开完整转录（68分34秒完整版，中英双语）

视频全文转录（中英双语）

以下为完整中英双语转录，已加标点。英文在前，中文在后，逐段对照。

由 Groq Whisper 转录 → M2.7 B 方案整文标点 + 分段 → M2.7 段号保留翻译 → 逐段对照。

[段 1]

So this is Game Theory Economics 159. If you’re here for Art History, you’re either in the wrong room or stay anyway. Maybe this is the right room, but this is Game Theory, okay? You should have four handouts. Everyone should have four handouts. There is a legal release form. We’ll talk about it in a minute, about the videoing. There is a syllabus, which is a preliminary syllabus. It’s also online, and there are two games, labelled Game 1 and Game 2. Can I get you all to look at Game 1 and start thinking about it? And while you’re thinking about it, I’m hoping you can multitask a bit, and I’ll describe a bit about the class, and we’ll get a bit of admin under our belts. But please try and look at, if somebody’s not looking at it because they’re using it as a fan here, so look at Game 1 and fill out that form for me, okay? So while you’re filling that out, let me tell you a little bit about what we’re going to be doing here. So what is game theory? Game theory is a method of studying strategic situations. Okay, so what’s a strategic situation? Well, let’s start off with what’s not a strategic situation. In your economics, in your intro economics class in 115 or 110, you saw some pretty good examples of situations that were not strategic.

耶鲁大学博弈论公开课 - 第2集沉默，信令和苦难教育

Thu, 11 Jun 2026 00:29:00 +0800

视频信息

标题: 耶鲁大学博弈论公开课 - 第2集沉默，信令和苦难教育
BV号: BV1u54y1k74g
分集: p2
时长: 70分37秒（4237秒）
作者/来源: 耶鲁大学公开课
原始链接: B站视频
转录方式: Groq Whisper 英文转录；英文在前，中文在后逐段对照。

视频摘要

本集是耶鲁大学博弈论公开课第 2 集，主题为“沉默，信令和苦难教育”。课程以英文课堂讲授和互动讨论为主体，围绕信号与沉默展开，逐步引入博弈论中关于策略、收益、信息、均衡和动态推理的分析框架。本文提供英文原文与中文译文逐段对照，便于跟读、检索和复习。

核心要点

信号与沉默：本集围绕“沉默，信令和苦难教育”展开，是理解后续博弈论模型和课堂案例的基础。
信息不对称：讲授重点放在参与者如何根据目标、信息和他人行为选择策略。
教育作为信号：课堂通过案例、提问或推导展示抽象模型如何落到具体决策情境。
策略性沟通：内容强调从结果反推策略条件，训练形式化的战略思维。

点击展开完整转录（70分37秒完整版，中英双语）

视频全文转录（中英双语）

以下为完整中英双语转录，已加标点。英文在前，中文在后，逐段对照。

由 Groq Whisper 转录 → M2.7 B 方案整文标点 + 分段 → M2.7 段号保留翻译 → 逐段对照。

[段 1]

Okay, so today we’re going to study asymmetric information, it’s our last week, and we’re going to focus on signaling today, and I’ll spell it with one L here as a concessions to the Americans. All right, so we’re going to divide this class into two parts, and for the first part, we’re going to focus on the case where there is some verifiable, verifiable information. in the problem. Alright, so we’ll see what this means in a while, but let me just set up an example and we’ll see where that takes us. So I want to return to a game we know well by this stage, which is the Cournot game. So there’s two firms, and they’re competing in Cournot, so they’re competing in quantities. And we’ll call the firms A and B. And suppose that firm B has costs so to be more formal these are constant marginal costs are equal to Cm where m means middle or medium or something and firm A firm A also has costs but those costs could come in one of three types it could be that firm A has high costs and high costs are equal to middle costs plus a little bit. And it could be that firm A also has medium costs, and it could be that firm A has low costs. And the low costs are just the medium costs minus a little bit.

耶鲁大学博弈论公开课 - 第3集拍卖和获奖者的诅咒

Thu, 11 Jun 2026 00:28:00 +0800

视频信息

标题: 耶鲁大学博弈论公开课 - 第3集拍卖和获奖者的诅咒
BV号: BV1u54y1k74g
分集: p3
时长: 62分28秒（3748秒）
作者/来源: 耶鲁大学公开课
原始链接: B站视频
转录方式: Groq Whisper 英文转录；英文在前，中文在后逐段对照。

视频摘要

本集是耶鲁大学博弈论公开课第 3 集，主题为“拍卖和获奖者的诅咒”。课程以英文课堂讲授和互动讨论为主体，围绕拍卖机制展开，逐步引入博弈论中关于策略、收益、信息、均衡和动态推理的分析框架。本文提供英文原文与中文译文逐段对照，便于跟读、检索和复习。

核心要点

拍卖机制：本集围绕“拍卖和获奖者的诅咒”展开，是理解后续博弈论模型和课堂案例的基础。
出价策略：讲授重点放在参与者如何根据目标、信息和他人行为选择策略。
获胜者诅咒：课堂通过案例、提问或推导展示抽象模型如何落到具体决策情境。
共同价值与私人价值：内容强调从结果反推策略条件，训练形式化的战略思维。

点击展开完整转录（62分28秒完整版，中英双语）

视频全文转录（中英双语）

以下为完整中英双语转录，已加标点。英文在前，中文在后，逐段对照。

由 Groq Whisper 转录 → M2.7 B 方案整文标点 + 分段 → M2.7 段号保留翻译 → 逐段对照。

[段 1]

Where have my jars of coins got to? That isn’t very far. They’ve only been along one row. All right, we’ll whiz them along this row as fast as you can. Just shake and pass now. Everybody who has had access to those jars, can you please write down on your notebook, just write down, but don’t show it to your neighbor, write down for each of those two jars how many coins you think are in the small jar and how many coins you think are in the large jar. How many coins you think are in the small jar and how many coins you think are in the large jar. Keep passing it along. So today I want to talk about auctions. And just to put this in the context of the whole class, way back on the very first day the class we talked about different types of people playing games. We talked about evil gits versus indignant angels. And then for most of the course, really until this week, we’ve been assuming that you knew who it was you were playing You knew your own payoffs but you also knew who it was you were playing against or with But the new feature of this week has been that we looking at settings where you don’t necessarily know what are the payoffs of the other people involved in the game or strategic situation.

耶鲁大学博弈论公开课 - 第4集作弊，惩罚和外包

Thu, 11 Jun 2026 00:27:00 +0800

视频信息

标题: 耶鲁大学博弈论公开课 - 第4集作弊，惩罚和外包
BV号: BV1u54y1k74g
分集: p4
时长: 75分47秒（4547秒）
作者/来源: 耶鲁大学公开课
原始链接: B站视频
转录方式: Groq Whisper 英文转录；英文在前，中文在后逐段对照。

视频摘要

本集是耶鲁大学博弈论公开课第 4 集，主题为“作弊，惩罚和外包”。课程以英文课堂讲授和互动讨论为主体，围绕作弊与惩罚展开，逐步引入博弈论中关于策略、收益、信息、均衡和动态推理的分析框架。本文提供英文原文与中文译文逐段对照，便于跟读、检索和复习。

核心要点

作弊与惩罚：本集围绕“作弊，惩罚和外包”展开，是理解后续博弈论模型和课堂案例的基础。
激励约束：讲授重点放在参与者如何根据目标、信息和他人行为选择策略。
外包关系：课堂通过案例、提问或推导展示抽象模型如何落到具体决策情境。
制度设计：内容强调从结果反推策略条件，训练形式化的战略思维。

点击展开完整转录（75分47秒完整版，中英双语）

视频全文转录（中英双语）

以下为完整中英双语转录，已加标点。英文在前，中文在后，逐段对照。

由 Groq Whisper 转录 → M2.7 B 方案整文标点 + 分段 → M2.7 段号保留翻译 → 逐段对照。

[段 1]

So last time, we were focusing on repeated interaction, and that’s what we’re going to continue with today. There’s lots of things we could study under repeated interaction, but the emphasis of this week is, can we attain and achieve cooperation in business or personal relationships without contracts by use of the fact that these relationships go on over time? And our central intuition, where we started from last time, was perhaps the future of a relationship can provide incentives for good behavior today. Can provide incentives for people not to cheat. So specifically, let’s think of an example, and we’ll go back to where we were last time. Specifically, suppose I have a business relationship, an ongoing business relationship with Jake. And each period I’m supposed to supply Jake with some inputs for his business, let’s say some fruit, and each period he’s supposed to provide me with some input for my business, namely vegetables. And clearly there are opportunities here in each period for us to cheat. We could cheat both on the quality of the fruit that I provide or the quantity of the fruit that I provide to Jake and he can cheat on the quantity or quality of the vegetables that he provides to me Our central intuition is perhaps what can work is, what can give us good incentives is, the idea that if Jake cooperates today, then I might cooperate tomorrow.

耶鲁大学博弈论公开课 - 第5集战争的消耗

Thu, 11 Jun 2026 00:26:00 +0800

视频信息

标题: 耶鲁大学博弈论公开课 - 第5集战争的消耗
BV号: BV1u54y1k74g
分集: p5
时长: 75分36秒（4536秒）
作者/来源: 耶鲁大学公开课
原始链接: B站视频
转录方式: Groq Whisper 英文转录；英文在前，中文在后逐段对照。

视频摘要

本集是耶鲁大学博弈论公开课第 5 集，主题为“战争的消耗”。课程以英文课堂讲授和互动讨论为主体，围绕战争消耗模型展开，逐步引入博弈论中关于策略、收益、信息、均衡和动态推理的分析框架。本文提供英文原文与中文译文逐段对照，便于跟读、检索和复习。

核心要点

战争消耗模型：本集围绕“战争的消耗”展开，是理解后续博弈论模型和课堂案例的基础。
承诺与成本：讲授重点放在参与者如何根据目标、信息和他人行为选择策略。
动态博弈：课堂通过案例、提问或推导展示抽象模型如何落到具体决策情境。
战略耐心：内容强调从结果反推策略条件，训练形式化的战略思维。

点击展开完整转录（75分36秒完整版，中英双语）

视频全文转录（中英双语）

以下为完整中英双语转录，已加标点。英文在前，中文在后，逐段对照。

由 Groq Whisper 转录 → M2.7 B 方案整文标点 + 分段 → M2.7 段号保留翻译 → 逐段对照。

[段 1]

Last time we looked at how to apply our new idea, sub-game perfect equilibrium, to a whole bunch of games. And our general idea for how to solve for sub-game perfect equilibrium was as follows. We looked at each sub-game. We solved for the Nash equilibrium in the sub-game, something we learned to do long ago. And then we rolled back the payoffs. We rolled them back up the tree. and towards the end we learned something interesting I’m not going to go back to it today I just want to emphasize it we learned that strategic effects matter so in that investment game we looked at last time when you were considering whether to rent a new piece of machinery it made a very big difference whether you considered how this action would affect the actions of the other side in this case how it affects your competition and this is a very general idea very general point So just to give you a couple of more examples, when you’re designing tax systems, I mentioned this last time, when you’re designing a tax system, make some changes in the U.S. tax system, it’s not good enough to look at how people are behaving in the old tax system and just calculate in an accounting manner how much more money you’re going to raise or how much money it’s going to cost you.

耶鲁大学博弈论公开课 - 第6集信息集和子博弈完美

Thu, 11 Jun 2026 00:25:00 +0800

视频信息

标题: 耶鲁大学博弈论公开课 - 第6集信息集和子博弈完美
BV号: BV1u54y1k74g
分集: p6
时长: 75分58秒（4558秒）
作者/来源: 耶鲁大学公开课
原始链接: B站视频
转录方式: Groq Whisper 英文转录；英文在前，中文在后逐段对照。

视频摘要

本集是耶鲁大学博弈论公开课第 6 集，主题为“信息集和子博弈完美”。课程以英文课堂讲授和互动讨论为主体，围绕信息集展开，逐步引入博弈论中关于策略、收益、信息、均衡和动态推理的分析框架。本文提供英文原文与中文译文逐段对照，便于跟读、检索和复习。

核心要点

信息集：本集围绕“信息集和子博弈完美”展开，是理解后续博弈论模型和课堂案例的基础。
子博弈完美：讲授重点放在参与者如何根据目标、信息和他人行为选择策略。
逆向归纳：课堂通过案例、提问或推导展示抽象模型如何落到具体决策情境。
动态一致性：内容强调从结果反推策略条件，训练形式化的战略思维。

点击展开完整转录（75分58秒完整版，中英双语）

视频全文转录（中英双语）

以下为完整中英双语转录，已加标点。英文在前，中文在后，逐段对照。

由 Groq Whisper 转录 → M2.7 B 方案整文标点 + 分段 → M2.7 段号保留翻译 → 逐段对照。

[段 1]

So today we have a lot of stuff to get through, but it’s all going to be fairly formal. We’re not going to have time to play a game today. Today’s going to be a day where we have to learn some new ideas. So the reason we need to go through some new formal ideas today is we’ve kind of exhausted what we can do with the ideas we’ve gathered so far. So just to bring us up to date where we are, in the first half of the semester, so before the midterm, we looked at simultaneous move games, and one way to think about those simultaneous move games were games where when I make my choice, I don’t know what you’ve done. And when you make your choice, you don’t know what I’ve done. And since the midterm, we’ve been looking at simple examples of sequential move games, sequential move games under perfect information, in which I typically do know what you did when I get to make my choice. And you know I’m going to know what you did when I get to make my choice. And what I want to be able to do moving forward is I want to be able to look at strategic situations that combine those two settings. I want to be able to analyze games which involve both sequential moves and simultaneous move games And in particular I want to see how we can extend the technique we been focusing on for the last few weeks which is backward induction I want us to see how we can extend the notion of backward induction to cope with games where some parts are sequential and some parts are simultaneous.

耶鲁大学博弈论公开课 - 第7集合作与结局

Thu, 11 Jun 2026 00:24:00 +0800

视频信息

标题: 耶鲁大学博弈论公开课 - 第7集合作与结局
BV号: BV1u54y1k74g
分集: p7
时长: 75分19秒（4519秒）
作者/来源: 耶鲁大学公开课
原始链接: B站视频
转录方式: Groq Whisper 英文转录；英文在前，中文在后逐段对照。

视频摘要

本集是耶鲁大学博弈论公开课第 7 集，主题为“合作与结局”。课程以英文课堂讲授和互动讨论为主体，围绕合作与重复博弈展开，逐步引入博弈论中关于策略、收益、信息、均衡和动态推理的分析框架。本文提供英文原文与中文译文逐段对照，便于跟读、检索和复习。

核心要点

合作与重复博弈：本集围绕“合作与结局”展开，是理解后续博弈论模型和课堂案例的基础。
终局效应：讲授重点放在参与者如何根据目标、信息和他人行为选择策略。
信誉机制：课堂通过案例、提问或推导展示抽象模型如何落到具体决策情境。
长期互动：内容强调从结果反推策略条件，训练形式化的战略思维。

点击展开完整转录（75分19秒完整版，中英双语）

视频全文转录（中英双语）

以下为完整中英双语转录，已加标点。英文在前，中文在后，逐段对照。

由 Groq Whisper 转录 → M2.7 B 方案整文标点 + 分段 → M2.7 段号保留翻译 → 逐段对照。

[段 1]

Okay, let’s make a start. So I hope everyone had a good break. We’re going to spend this week looking at repeated interaction. Now we already saw last time before the break that once we repeat games, once games go on for a while we can sustain behavior that’s quite interesting So for example before the break we saw that we could sustain fighting by players that were rational in a war of attrition alright and another thing we learned before the break was when we’re analyzing these potentially very long games it helps sometimes to break it break the analysis up into what we might call stage games each each period of the game and break the payoffs up into the payoffs that are associated with that stage payoffs that are associated with the past but they’re sunk they don’t really matter and payoffs that are going to come in the future from future equilibrium play so those are some ideas we going to pick up today but for the most part what we do today will be new Now whereas last time we focused on fighting for the whole of today I want to focus on the issue of cooperation In fact, for the whole of this week I want to focus on the issue of cooperation. And the question kind of behind everything this week is going to be, can repeated interaction among players both induce and sustain cooperative behavior, or if you like, good behavior.

耶鲁大学博弈论公开课 - 第8集落后的感应-国际象棋，战略和可信的威胁

Thu, 11 Jun 2026 00:23:00 +0800

视频信息

标题: 耶鲁大学博弈论公开课 - 第8集落后的感应-国际象棋，战略和可信的威胁
BV号: BV1u54y1k74g
分集: p8
时长: 72分39秒（4359秒）
作者/来源: 耶鲁大学公开课
原始链接: B站视频
转录方式: Groq Whisper 英文转录；英文在前，中文在后逐段对照。

视频摘要

本集是耶鲁大学博弈论公开课第 8 集，主题为“落后的感应-国际象棋，战略和可信的威胁”。课程以英文课堂讲授和互动讨论为主体，围绕逆向归纳展开，逐步引入博弈论中关于策略、收益、信息、均衡和动态推理的分析框架。本文提供英文原文与中文译文逐段对照，便于跟读、检索和复习。

核心要点

逆向归纳：本集围绕“落后的感应-国际象棋，战略和可信的威胁”展开，是理解后续博弈论模型和课堂案例的基础。
国际象棋式推理：讲授重点放在参与者如何根据目标、信息和他人行为选择策略。
可信威胁：课堂通过案例、提问或推导展示抽象模型如何落到具体决策情境。
战略承诺：内容强调从结果反推策略条件，训练形式化的战略思维。

点击展开完整转录（72分39秒完整版，中英双语）

视频全文转录（中英双语）

以下为完整中英双语转录，已加标点。英文在前，中文在后，逐段对照。

由 Groq Whisper 转录 → M2.7 B 方案整文标点 + 分段 → M2.7 段号保留翻译 → 逐段对照。

[段 1]

So last time we finished up by playing the game of NIMH. And you’ll remember, I hope, that the game of NIMH was a game where there was two piles of stones. We made do with lines on the board. And the winner was the person who picked up the last stone. Remember, you have to pick piles. And I want to use the game of NIMH to make a transition here. So what we pointed out about the game of NIMH game was it illustrated very nicely for us that games can have first mover advantages or they can have second mover advantages. A very small change in the game, essentially a very small change in where we started from could switch a game from a game with a first mover advantage to a game with a second mover advantage. Alright? Now today I want to make, just draw a slightly grander lesson out of that game. So not only was it the case that the game sometimes has first mover advantages and sometimes has second mover advantages. But moreover, we could tell when it had a first mover advantage and we could tell when it had a second mover advantage. Is that right? When we actually looked at the initial setup of those stones we knew immediately that a game in which player 1 is going to win or alternatively we knew immediately that a game in which player 2 is going to win Alright?

耶鲁大学博弈论公开课 - 第9集进化稳定-合作，突变，与平衡

Thu, 11 Jun 2026 00:22:00 +0800

视频信息

标题: 耶鲁大学博弈论公开课 - 第9集进化稳定-合作，突变，与平衡
BV号: BV1u54y1k74g
分集: p9
时长: 72分20秒（4340秒）
作者/来源: 耶鲁大学公开课
原始链接: B站视频
转录方式: Groq Whisper 英文转录；英文在前，中文在后逐段对照。

视频摘要

本集是耶鲁大学博弈论公开课第 9 集，主题为“进化稳定-合作，突变，与平衡”。课程以英文课堂讲授和互动讨论为主体，围绕进化稳定策略展开，逐步引入博弈论中关于策略、收益、信息、均衡和动态推理的分析框架。本文提供英文原文与中文译文逐段对照，便于跟读、检索和复习。

核心要点

进化稳定策略：本集围绕“进化稳定-合作，突变，与平衡”展开，是理解后续博弈论模型和课堂案例的基础。
合作与突变：讲授重点放在参与者如何根据目标、信息和他人行为选择策略。
均衡选择：课堂通过案例、提问或推导展示抽象模型如何落到具体决策情境。
演化博弈：内容强调从结果反推策略条件，训练形式化的战略思维。

点击展开完整转录（72分20秒完整版，中英双语）

视频全文转录（中英双语）

以下为完整中英双语转录，已加标点。英文在前，中文在后，逐段对照。

由 Groq Whisper 转录 → M2.7 B 方案整文标点 + 分段 → M2.7 段号保留翻译 → 逐段对照。

[段 1]

So we’re going to do a new topic today. We’re going to talk about evolution. We’re going to talk about the connection between evolution and game theory. All right, now there’s going to be an extra, I already emailed you about this, there’s going to be an extra reading on this for the people who want it. I’m going to, there’s a reading packet that’s available to anybody who wants it. I emailed you all the websites where you can order that reading packet and find, and figure out where to pick it up. It’s not compulsory, you don’t have to look at that reading packet, it’s just it might help. In addition, as with last Wednesday, since some of the material here is new, I have written a handout that goes with this lecture, and that handout will appear magically this afternoon on the website All right So things today are fast Don worry There a handout that goes with it All right so why look at evolution in the context of game theory There are really two reasons. The first reason is because of the influence of game theory on biology. It turns out that in the last few decades, there’s been an enormous amount of work done in biology, in particular looking at animal behavior and using game theory to analyze that animal behavior. And just to give you a loose idea about how this works, the idea is to relate strategies with genes, or at least the phenotype of those genes, and to relate payoffs to genetic fitness.

耶鲁大学博弈论公开课 - 第10集混合战略棒球，约会和支付您的税

Thu, 11 Jun 2026 00:21:00 +0800

视频信息

标题: 耶鲁大学博弈论公开课 - 第10集混合战略棒球，约会和支付您的税
BV号: BV1u54y1k74g
分集: p10
时长: 73分45秒（4425秒）
作者/来源: 耶鲁大学公开课
原始链接: B站视频
转录方式: Groq Whisper 英文转录；英文在前，中文在后逐段对照。

视频摘要

本集是耶鲁大学博弈论公开课第 10 集，主题为“混合战略棒球，约会和支付您的税”。课程以英文课堂讲授和互动讨论为主体，围绕混合策略展开，逐步引入博弈论中关于策略、收益、信息、均衡和动态推理的分析框架。本文提供英文原文与中文译文逐段对照，便于跟读、检索和复习。

核心要点

混合策略：本集围绕“混合战略棒球，约会和支付您的税”展开，是理解后续博弈论模型和课堂案例的基础。
随机化：讲授重点放在参与者如何根据目标、信息和他人行为选择策略。
无差异条件：课堂通过案例、提问或推导展示抽象模型如何落到具体决策情境。
均衡计算：内容强调从结果反推策略条件，训练形式化的战略思维。

点击展开完整转录（73分45秒完整版，中英双语）

视频全文转录（中英双语）

以下为完整中英双语转录，已加标点。英文在前，中文在后，逐段对照。

由 Groq Whisper 转录 → M2.7 B 方案整文标点 + 分段 → M2.7 段号保留翻译 → 逐段对照。

[段 1]

All right, so last time we did something I think substantially harder than anything we’ve done in the class so far. We looked at mixed strategies and in particular we looked at mixed strategy equilibrium. All right? And there was a big idea last time. The big idea was if a player is playing a mixed strategy in equilibrium, then every pure strategy in the mix, that’s to say every pure strategy on which they place some positive weight, must also be a best response to what the other side is doing. And then we used that trick, we used it in this game here, to help us find Nash equilibria. And the way it allowed us to find Nash equilibria is we knew that if, in this case, Venus Williams is mixing between left and right, it must be this case that her payoff is equal to that of right And we used that to find Serena mix And conversely since we knew that Serena is mixing again between little l and little r we knew she must be indifferent between little l and little r and we used that to find Venus’s mix. So I want to go back to this example just for a few moments, just to make one more point, and then we’ll move on. But we’ll still be talking about mix strategies throughout today.

耶鲁大学博弈论公开课 - 第11集落后的感应-声誉和决斗

Thu, 11 Jun 2026 00:20:00 +0800

视频信息

标题: 耶鲁大学博弈论公开课 - 第11集落后的感应-声誉和决斗
BV号: BV1u54y1k74g
分集: p11
时长: 75分56秒（4556秒）
作者/来源: 耶鲁大学公开课
原始链接: B站视频
转录方式: Groq Whisper 英文转录；英文在前，中文在后逐段对照。

视频摘要

本集是耶鲁大学博弈论公开课第 11 集，主题为“落后的感应-声誉和决斗”。课程以英文课堂讲授和互动讨论为主体，围绕不完全信息展开，逐步引入博弈论中关于策略、收益、信息、均衡和动态推理的分析框架。本文提供英文原文与中文译文逐段对照，便于跟读、检索和复习。

核心要点

不完全信息：本集围绕“落后的感应-声誉和决斗”展开，是理解后续博弈论模型和课堂案例的基础。
贝叶斯推断：讲授重点放在参与者如何根据目标、信息和他人行为选择策略。
信念更新：课堂通过案例、提问或推导展示抽象模型如何落到具体决策情境。
策略选择：内容强调从结果反推策略条件，训练形式化的战略思维。

点击展开完整转录（75分56秒完整版，中英双语）

视频全文转录（中英双语）

以下为完整中英双语转录，已加标点。英文在前，中文在后，逐段对照。

由 Groq Whisper 转录 → M2.7 B 方案整文标点 + 分段 → M2.7 段号保留翻译 → 逐段对照。

[段 1]

Tanya Cushman Reviewer’s Name Reviewer’s Name Okay, so this is what we did last time. We looked at a game involving an entrance and an incumbent in a market. And the entrance had to decide whether to enter that market or not, And if they stayed out, the incumbent remained a monopolist, and the monopolist made three million in profit. All right? And if the entrant goes in, then the incumbent can decide whether to accommodate the entrant and just settle for duopoly profits, making a million each, or the incumbent can fight, in which case the incumbent makes no money at all, and the entrant loses a million dollars. And we pointed out a number of things about this game. was that when we analyzed it in a matrix form, we quickly found that there were two Nash equilibria. Nash equilibria were in and not fight, and out and fight. But we argued that backward induction tells us that the sensible answer is in and not fight Once the incumbent knows the entrant is in they not going to fight because one is bigger than zero and the entrant anticipating this will enter And we talked a little bit more, we said this other equilibrium, this out-fight equilibrium, it is an equilibrium because if the entrant believes the incumbent is going to fight, then the entrant is going to stay out, and it’s costless for the incumbent to, quote, fight if in fact the entrant does stay out because they never get called upon to fight anyway.

耶鲁大学博弈论公开课 - 第12集进化稳定-社会公约，侵略，和周期

Thu, 11 Jun 2026 00:19:00 +0800

视频信息

标题: 耶鲁大学博弈论公开课 - 第12集进化稳定-社会公约，侵略，和周期
BV号: BV1u54y1k74g
分集: p12
时长: 66分20秒（3980秒）
作者/来源: 耶鲁大学公开课
原始链接: B站视频
转录方式: Groq Whisper 英文转录；英文在前，中文在后逐段对照。

视频摘要

本集是耶鲁大学博弈论公开课第 12 集，主题为“进化稳定-社会公约，侵略，和周期”。课程以英文课堂讲授和互动讨论为主体，围绕协调问题展开，逐步引入博弈论中关于策略、收益、信息、均衡和动态推理的分析框架。本文提供英文原文与中文译文逐段对照，便于跟读、检索和复习。

核心要点

协调问题：本集围绕“进化稳定-社会公约，侵略，和周期”展开，是理解后续博弈论模型和课堂案例的基础。
多重均衡：讲授重点放在参与者如何根据目标、信息和他人行为选择策略。
制度与预期：课堂通过案例、提问或推导展示抽象模型如何落到具体决策情境。
博弈论应用：内容强调从结果反推策略条件，训练形式化的战略思维。

点击展开完整转录（66分20秒完整版，中英双语）

视频全文转录（中英双语）

以下为完整中英双语转录，已加标点。英文在前，中文在后，逐段对照。

由 Groq Whisper 转录 → M2.7 B 方案整文标点 + 分段 → M2.7 段号保留翻译 → 逐段对照。

[段 1]

All right, so this was the definition we saw at the end last time. I tried to write it a bit larger. I just repeat the second of those definitions. This is the definition that connects the notion of evolutionary stability, for now in pure strategies with Nash equilibrium. And basically it says this, to check whether a strategy is evolutionally stable in pure strategies, first check whether S hat, S hat is a symmetric Nash equilibrium. And if it is, if it’s a strict Nash equilibrium, we’re done. And if it’s not strict, that means there’s at least some other strategy that would tie with S hat against S hat. then compare how s-hat does against this mutation with how the mutation does against itself. And if s-hat does better than the mutation than the mutation does against itself, then we’re okay. And one virtue of this definition is it very easy to check so let try an example to see that And also to get us back into gear and reminding ourselves what we’re doing a bit. All right, so in this example, it’s a sort of trivial game, but still, the game looks like this. All right, and we’re asked, since we’re asked the question, what is evolutionarily stable in this game? So no prizes for finding the symmetric Nash equilibrium in this game. Shout it out.

耶鲁大学博弈论公开课 - 第13集顺序游戏-道德风险，奖励和饥饿的狮子

Thu, 11 Jun 2026 00:18:00 +0800

视频信息

标题: 耶鲁大学博弈论公开课 - 第13集顺序游戏-道德风险，奖励和饥饿的狮子
BV号: BV1u54y1k74g
分集: p13
时长: 70分47秒（4247秒）
作者/来源: 耶鲁大学公开课
原始链接: B站视频
转录方式: Groq Whisper 英文转录；英文在前，中文在后逐段对照。

视频摘要

本集是耶鲁大学博弈论公开课第 13 集，主题为“顺序游戏-道德风险，奖励和饥饿的狮子”。课程以英文课堂讲授和互动讨论为主体，围绕顺序游戏-道德风险，奖励和饥饿的狮子展开，逐步引入博弈论中关于策略、收益、信息、均衡和动态推理的分析框架。本文提供英文原文与中文译文逐段对照，便于跟读、检索和复习。

核心要点

顺序游戏-道德风险，奖励和饥饿的狮子：本集围绕“顺序游戏-道德风险，奖励和饥饿的狮子”展开，是理解后续博弈论模型和课堂案例的基础。
核心概念：讲授重点放在参与者如何根据目标、信息和他人行为选择策略。
课堂案例：课堂通过案例、提问或推导展示抽象模型如何落到具体决策情境。
策略推理：内容强调从结果反推策略条件，训练形式化的战略思维。

点击展开完整转录（70分47秒完整版，中英双语）

视频全文转录（中英双语）

以下为完整中英双语转录，已加标点。英文在前，中文在后，逐段对照。

由 Groq Whisper 转录 → M2.7 B 方案整文标点 + 分段 → M2.7 段号保留翻译 → 逐段对照。

[段 1]

Okay, so I want to set up a new topic today, and to get us started I thought we’d play a game. So the game is going to be called Cash and a Hat, and we’ll see what this game is like in a minute. so the idea is this, there’s going to be two players I’m going to pick on two of you I hope I can find people who brought some money to class alright, so player one will have a choice player one can put nothing one dollar or three dollars into a hat the hat will then be given to player two and player two can look at what’s in the hat and either she can match what’s in the hat, i.e. add the same amount in, so one if it’s one or three if it’s three, or she can simply take the cash. All right, the payoff of this game will be as follows. Player one, if they put nothing in, they’re not going to get anything If they put one in and it matched then they double their money so they get two back If they put three in and it matched then they double their money so they get six back they’ll net three. However, if they put one in and player two takes it, they’ve just lost their dollar. And if they put three dollars in and player two takes it, they’ve lost three dollars.

耶鲁大学博弈论公开课 - 第14集落后的感应-承诺，间谍，和先行者优势

Thu, 11 Jun 2026 00:17:00 +0800

视频信息

标题: 耶鲁大学博弈论公开课 - 第14集落后的感应-承诺，间谍，和先行者优势
BV号: BV1u54y1k74g
分集: p14
时长: 67分21秒（4041秒）
作者/来源: 耶鲁大学公开课
原始链接: B站视频
转录方式: Groq Whisper 英文转录；英文在前，中文在后逐段对照。

视频摘要

本集是耶鲁大学博弈论公开课第 14 集，主题为“落后的感应-承诺，间谍，和先行者优势”。课程以英文课堂讲授和互动讨论为主体，围绕落后的感应-承诺，间谍，和先行者优势展开，逐步引入博弈论中关于策略、收益、信息、均衡和动态推理的分析框架。本文提供英文原文与中文译文逐段对照，便于跟读、检索和复习。

核心要点

落后的感应-承诺，间谍，和先行者优势：本集围绕“落后的感应-承诺，间谍，和先行者优势”展开，是理解后续博弈论模型和课堂案例的基础。
核心概念：讲授重点放在参与者如何根据目标、信息和他人行为选择策略。
课堂案例：课堂通过案例、提问或推导展示抽象模型如何落到具体决策情境。
策略推理：内容强调从结果反推策略条件，训练形式化的战略思维。

点击展开完整转录（67分21秒完整版，中英双语）

视频全文转录（中英双语）

以下为完整中英双语转录，已加标点。英文在前，中文在后，逐段对照。

由 Groq Whisper 转录 → M2.7 B 方案整文标点 + 分段 → M2.7 段号保留翻译 → 逐段对照。

[段 1]

All right, so today I want to do something a little bit more mundane than we did on Monday. I want to go back and talk about quantity competition. so in the first half of the course we talked about price competition we talked about quantity competition we talked about competition with differentiated products I want to go back and revisit essentially the Cournot model so this was the Cournot model two firms are producing are choosing their quantities simultaneously firm 1 is choosing Q1 and firm 2 is choosing Q2 and all of this is just reviews so this is all stuff that’s in your notes already already, this is the demand curve. It tells us that prices depend on the total quantity being produced. So this is Q1 plus Q2, and this is prices. Then the demand curve is a straight line of slope B. All right that what this tells us It has slope minus B All right And we know that payoffs are just profits which are price times quantity revenues minus cost times quantity costs. We’ll get assuming constant marginal costs. And we did this model out in full in maybe the third week of class, and we figured out what the best response diagram looked like.

耶鲁大学博弈论公开课 - 第15集迭代剔除和中位选民定理

Thu, 11 Jun 2026 00:16:00 +0800

视频信息

标题: 耶鲁大学博弈论公开课 - 第15集迭代剔除和中位选民定理
BV号: BV1u54y1k74g
分集: p15
时长: 61分32秒（3692秒）
作者/来源: 耶鲁大学公开课
原始链接: B站视频
转录方式: Groq Whisper 英文转录；英文在前，中文在后逐段对照。

视频摘要

本集是耶鲁大学博弈论公开课第 15 集，主题为“迭代剔除和中位选民定理”。课程以英文课堂讲授和互动讨论为主体，围绕迭代剔除和中位选民定理展开，逐步引入博弈论中关于策略、收益、信息、均衡和动态推理的分析框架。本文提供英文原文与中文译文逐段对照，便于跟读、检索和复习。

核心要点

迭代剔除和中位选民定理：本集围绕“迭代剔除和中位选民定理”展开，是理解后续博弈论模型和课堂案例的基础。
核心概念：讲授重点放在参与者如何根据目标、信息和他人行为选择策略。
课堂案例：课堂通过案例、提问或推导展示抽象模型如何落到具体决策情境。
策略推理：内容强调从结果反推策略条件，训练形式化的战略思维。

点击展开完整转录（61分32秒完整版，中英双语）

视频全文转录（中英双语）

以下为完整中英双语转录，已加标点。英文在前，中文在后，逐段对照。

由 Groq Whisper 转录 → M2.7 B 方案整文标点 + 分段 → M2.7 段号保留翻译 → 逐段对照。

[段 1]

Last time, we talked a lot about the idea, I didn’t mention the name, but here’s some jargon for you, we talked about the idea of deleting dominated strategies, looking at a game, figuring out which strategies are dominated, deleting them, looking at the game again, looking at which strategies are now dominated, deleting those, and so on and so forth. And this process is called the iterative deletion of dominated strategies. This is not a great title for Barry’s book. You’d be better than that to get the $250, right? This is a boring title. Whatever mind, iterative deletion of dominated strategies. The idea, it embodies the idea of putting yourself in someone else’s shoes and trying to figure out what they’re going to do, and then think about them, putting themselves in your shoes, figuring out what you’re going to do, and so on and so forth. And last time, we saw already that this is a very powerful idea, all right, in that game last time, but we also saw it’s a dangerous idea to take too literally, that sometimes this can get you to overthink the problem, and actually, as in that numbers game last time, the optimal, the best choice, the winning choice, might not involve so many rounds. All right, we also saw in that numbers game last time that in some games, but by no means all games, in some games, this process actually converges to a single choice in that numbers game, it converged to one.

耶鲁大学博弈论公开课 - 第16集学会换位思考

Thu, 11 Jun 2026 00:15:00 +0800

视频信息

标题: 耶鲁大学博弈论公开课 - 第16集学会换位思考
BV号: BV1u54y1k74g
分集: p16
时长: 69分01秒（4141秒）
作者/来源: 耶鲁大学公开课
原始链接: B站视频
转录方式: Groq Whisper 英文转录；英文在前，中文在后逐段对照。

视频摘要

本集是耶鲁大学博弈论公开课第 16 集，主题为“学会换位思考”。课程以英文课堂讲授和互动讨论为主体，围绕学会换位思考展开，逐步引入博弈论中关于策略、收益、信息、均衡和动态推理的分析框架。本文提供英文原文与中文译文逐段对照，便于跟读、检索和复习。

核心要点

学会换位思考：本集围绕“学会换位思考”展开，是理解后续博弈论模型和课堂案例的基础。
核心概念：讲授重点放在参与者如何根据目标、信息和他人行为选择策略。
课堂案例：课堂通过案例、提问或推导展示抽象模型如何落到具体决策情境。
策略推理：内容强调从结果反推策略条件，训练形式化的战略思维。

点击展开完整转录（69分01秒完整版，中英双语）

视频全文转录（中英双语）

以下为完整中英双语转录，已加标点。英文在前，中文在后，逐段对照。

由 Groq Whisper 转录 → M2.7 B 方案整文标点 + 分段 → M2.7 段号保留翻译 → 逐段对照。

[段 1]

Okay, so last time we looked at and played this game. You had to choose grades, sorry, you had to choose alpha and beta, and this table told us what outcome would arise. In particular, what grade you would get and what grade your pair would get. So for example, if you’d chosen beta and your pair had chosen alpha, then you would get a C and your pair would get an A. And one of the first things we pointed out is that this is not quite a game yet. It’s missing something. This has outcomes in it. It’s an outcome matrix. but it isn’t a game because for a game we need to know payoffs. Okay? And then we looked at some possible payoffs, and now it is a game. So this is a game, just to give you some more jargon, this is a normal form game, and here we’ve assumed the payoffs are those that arise if players only care about their own grades which I think was true for a lot of you It wasn true for the gentleman who sitting there now but it was true for a lot of people Alright and we pointed out that in this game alpha strictly dominates beta What do we mean by that? We mean that if these are your payoffs, no matter what your pair does, you attain a higher payoff from choosing alpha than you do from choosing beta.

耶鲁大学博弈论公开课 - 第17集足球比赛与商业合作之最佳对策

Thu, 11 Jun 2026 00:14:00 +0800

视频信息

标题: 耶鲁大学博弈论公开课 - 第17集足球比赛与商业合作之最佳对策
BV号: BV1u54y1k74g
分集: p17
时长: 72分17秒（4337秒）
作者/来源: 耶鲁大学公开课
原始链接: B站视频
转录方式: Groq Whisper 英文转录；英文在前，中文在后逐段对照。

视频摘要

本集是耶鲁大学博弈论公开课第 17 集，主题为“足球比赛与商业合作之最佳对策”。课程以英文课堂讲授和互动讨论为主体，围绕足球比赛与商业合作之最佳对策展开，逐步引入博弈论中关于策略、收益、信息、均衡和动态推理的分析框架。本文提供英文原文与中文译文逐段对照，便于跟读、检索和复习。

核心要点

足球比赛与商业合作之最佳对策：本集围绕“足球比赛与商业合作之最佳对策”展开，是理解后续博弈论模型和课堂案例的基础。
核心概念：讲授重点放在参与者如何根据目标、信息和他人行为选择策略。
课堂案例：课堂通过案例、提问或推导展示抽象模型如何落到具体决策情境。
策略推理：内容强调从结果反推策略条件，训练形式化的战略思维。

点击展开完整转录（72分17秒完整版，中英双语）

视频全文转录（中英双语）

以下为完整中英双语转录，已加标点。英文在前，中文在后，逐段对照。

由 Groq Whisper 转录 → M2.7 B 方案整文标点 + 分段 → M2.7 段号保留翻译 → 逐段对照。

[段 1]

So last time we introduced a new idea and the new idea was that of best response. And the idea was to think of a strategy that is the best you can do given your belief about what the other people are doing, what your opponents are doing, what other players are doing. And you could think of this belief as the belief that rationalizes that choice. So if you have a boss, and he or she is going to ask you why you chose the action you did, if you took the best response to some belief, you can say, I took this action because I believed other people were going to do this, and since that was the best you could do under that belief, that will hopefully keep your job. Alright, I promised that today we would look at the most important game in the world, and as announced last time, the most important game is the penalty kick game. So this is a game that occurs in soccer and just to give an idea of how important it is for those people who are unfortunate enough not to be soccer fans here the last World Cup was decided on penalty kicks. In England’s case, England goes out of every single World Cup and every single European competition because it loses on penalty kicks, usually to Germany, it has to be said.

耶鲁大学博弈论公开课 - 第18集纳什均衡之立场选择、种族隔离与策略随机化

Thu, 11 Jun 2026 00:13:00 +0800

视频信息

标题: 耶鲁大学博弈论公开课 - 第18集纳什均衡之立场选择、种族隔离与策略随机化
BV号: BV1u54y1k74g
分集: p18
时长: 74分02秒（4442秒）
作者/来源: 耶鲁大学公开课
原始链接: B站视频
转录方式: Groq Whisper 英文转录；英文在前，中文在后逐段对照。

视频摘要

本集是耶鲁大学博弈论公开课第 18 集，主题为“纳什均衡之立场选择、种族隔离与策略随机化”。课程以英文课堂讲授和互动讨论为主体，围绕纳什均衡之立场选择、种族隔离与策略随机化展开，逐步引入博弈论中关于策略、收益、信息、均衡和动态推理的分析框架。本文提供英文原文与中文译文逐段对照，便于跟读、检索和复习。

核心要点

纳什均衡之立场选择、种族隔离与策略随机化：本集围绕“纳什均衡之立场选择、种族隔离与策略随机化”展开，是理解后续博弈论模型和课堂案例的基础。
核心概念：讲授重点放在参与者如何根据目标、信息和他人行为选择策略。
课堂案例：课堂通过案例、提问或推导展示抽象模型如何落到具体决策情境。
策略推理：内容强调从结果反推策略条件，训练形式化的战略思维。

点击展开完整转录（74分02秒完整版，中英双语）

视频全文转录（中英双语）

以下为完整中英双语转录，已加标点。英文在前，中文在后，逐段对照。

由 Groq Whisper 转录 → M2.7 B 方案整文标点 + 分段 → M2.7 段号保留翻译 → 逐段对照。

[段 1]

So last time we left things in the middle of a model which was the candidate voter model. And what was, I don’t want to go over the whole model again, but just to iterate a little bit what was different about that model from what we saw before. And the main thing that was different was that the candidates cannot choose their positions. If you like, every voter is a potential candidate, but you know the positions of the voters. And let me just bring out two lessons that we left hanging last time. I want to put them on the board to make sure they’re in your notes. So the first lesson is, one thing we saw already last time, is there can be lots of different national equilibria in this model. There are multiple possible national equilibria in this model. and more to the point, not all of those equilibria have the candidates crowded at the center. Alright? We saw early on in the classic downed or median voter model that that model predicted crowding the center. This one doesn and we come back to that in a second And the second thing we saw last time was that entry can if you enter on the left one effect of entering on the left can be to make the candidate on the right more likely to win.

耶鲁大学博弈论公开课 - 第19集纳什均衡之伯川德模型与选民投票

Thu, 11 Jun 2026 00:12:00 +0800

视频信息

标题: 耶鲁大学博弈论公开课 - 第19集纳什均衡之伯川德模型与选民投票
BV号: BV1u54y1k74g
分集: p19
时长: 71分34秒（4294秒）
作者/来源: 耶鲁大学公开课
原始链接: B站视频
转录方式: Groq Whisper 英文转录；英文在前，中文在后逐段对照。

视频摘要

本集是耶鲁大学博弈论公开课第 19 集，主题为“纳什均衡之伯川德模型与选民投票”。课程以英文课堂讲授和互动讨论为主体，围绕纳什均衡之伯川德模型与选民投票展开，逐步引入博弈论中关于策略、收益、信息、均衡和动态推理的分析框架。本文提供英文原文与中文译文逐段对照，便于跟读、检索和复习。

核心要点

纳什均衡之伯川德模型与选民投票：本集围绕“纳什均衡之伯川德模型与选民投票”展开，是理解后续博弈论模型和课堂案例的基础。
核心概念：讲授重点放在参与者如何根据目标、信息和他人行为选择策略。
课堂案例：课堂通过案例、提问或推导展示抽象模型如何落到具体决策情境。
策略推理：内容强调从结果反推策略条件，训练形式化的战略思维。

点击展开完整转录（71分34秒完整版，中英双语）

视频全文转录（中英双语）

以下为完整中英双语转录，已加标点。英文在前，中文在后，逐段对照。

由 Groq Whisper 转录 → M2.7 B 方案整文标点 + 分段 → M2.7 段号保留翻译 → 逐段对照。

[段 1]

All right, so last time, we started to study imperfect competition. we looked at the Cournot model but the bigger theme the bigger theme is the study of how firms compete outside of the sort of easy cases that you study in 115 so outside of the example of monopoly where there is only one firm and so there’s not much competition and outside the case of perfect competition where there are so many firms it’s as if each firm is a price taker We’re going to continue with that today, and in fact you’re going to continue with it on into the homework. So last time we looked at Cournot, that was the model we started with. We looked at two firms competing in quantities, and just to review a little bit what we did last time kind of exercise there so I think is this right I think I probably went a little fast last time I was kicking myself afterwards I don know people can nod or shake their heads but I think I went a bit fast So I sorry for that but if there was a time to go too fast it was probably last time because it turns out this is something that’s covered very well in the textbook. So it’s covered in chapter 6 of the textbook.

耶鲁大学博弈论公开课 - 第20集纳什均衡之约会游戏与古诺模型

Thu, 11 Jun 2026 00:11:00 +0800

视频信息

标题: 耶鲁大学博弈论公开课 - 第20集纳什均衡之约会游戏与古诺模型
BV号: BV1u54y1k74g
分集: p20
时长: 72分19秒（4339秒）
作者/来源: 耶鲁大学公开课
原始链接: B站视频
转录方式: Groq Whisper 英文转录；英文在前，中文在后逐段对照。

视频摘要

本集是耶鲁大学博弈论公开课第 20 集，主题为“纳什均衡之约会游戏与古诺模型”。课程以英文课堂讲授和互动讨论为主体，围绕纳什均衡之约会游戏与古诺模型展开，逐步引入博弈论中关于策略、收益、信息、均衡和动态推理的分析框架。本文提供英文原文与中文译文逐段对照，便于跟读、检索和复习。

核心要点

纳什均衡之约会游戏与古诺模型：本集围绕“纳什均衡之约会游戏与古诺模型”展开，是理解后续博弈论模型和课堂案例的基础。
核心概念：讲授重点放在参与者如何根据目标、信息和他人行为选择策略。
课堂案例：课堂通过案例、提问或推导展示抽象模型如何落到具体决策情境。
策略推理：内容强调从结果反推策略条件，训练形式化的战略思维。

点击展开完整转录（72分19秒完整版，中英双语）

视频全文转录（中英双语）

以下为完整中英双语转录，已加标点。英文在前，中文在后，逐段对照。

由 Groq Whisper 转录 → M2.7 B 方案整文标点 + 分段 → M2.7 段号保留翻译 → 逐段对照。

[段 1]

All right, so last time we were talking about the investor game, and this was a coordination game. And we learned some things, I just want to recall some of the things we learned so I can highlight them a bit. one thing we learnt was that communication can help in a coordination game so I forget who it was but someone down here who’s disappeared was our Jimmy Stewart character and helped coordinate you on a better equilibrium simply by suggesting what you should do and there’s two lessons here one is this is very different from the prisoner’s dilemma So we learnt the very first time that in the prisoner’s dilemma communication per se won’t help but in a coordination problem which could be just as serious socially as a prisoner dilemma in a coordination problem it may well help and the reason it helps is you trying to coordinate onto a Nash equilibrium And one way to think about Nash equilibria is that they are self-enforcing agreements, so provided everyone believes that everyone else is going to go along with this agreement, then everyone in fact will. I want to make another slightly more philosophical remark associated with this, and it’s to do with the idea of leadership.

耶鲁大学博弈论公开课 - 第21集纳什均衡之坏风气与银行挤兑

Thu, 11 Jun 2026 00:10:00 +0800

视频信息

标题: 耶鲁大学博弈论公开课 - 第21集纳什均衡之坏风气与银行挤兑
BV号: BV1u54y1k74g
分集: p21
时长: 69分26秒（4166秒）
作者/来源: 耶鲁大学公开课
原始链接: B站视频
转录方式: Groq Whisper 英文转录；英文在前，中文在后逐段对照。

视频摘要

本集是耶鲁大学博弈论公开课第 21 集，主题为“纳什均衡之坏风气与银行挤兑”。课程以英文课堂讲授和互动讨论为主体，围绕纳什均衡之坏风气与银行挤兑展开，逐步引入博弈论中关于策略、收益、信息、均衡和动态推理的分析框架。本文提供英文原文与中文译文逐段对照，便于跟读、检索和复习。

核心要点

纳什均衡之坏风气与银行挤兑：本集围绕“纳什均衡之坏风气与银行挤兑”展开，是理解后续博弈论模型和课堂案例的基础。
核心概念：讲授重点放在参与者如何根据目标、信息和他人行为选择策略。
课堂案例：课堂通过案例、提问或推导展示抽象模型如何落到具体决策情境。
策略推理：内容强调从结果反推策略条件，训练形式化的战略思维。

点击展开完整转录（69分26秒完整版，中英双语）

视频全文转录（中英双语）

以下为完整中英双语转录，已加标点。英文在前，中文在后，逐段对照。

由 Groq Whisper 转录 → M2.7 B 方案整文标点 + 分段 → M2.7 段号保留翻译 → 逐段对照。

[段 1]

Okay, so last time we came across a new idea, although it wasn’t really new for a lot of you, and that was the idea of Nash equilibrium. and what I want to do today is discuss Nash equilibrium see how we find Nash equilibrium in some rather simple examples and then in the second half of today I want to look at an application where we actually have some fun and play a game which I hope it’s fun alright but let’s start by putting down a formal definition we only used a rather informal one last week so here’s a formal one a strategy profile Remember, profile is one strategy for each player, so it’s going to be S1 star, S2 star, all the way up to SN star, if there are N players playing the game. So this profile is a Nash equilibrium and I just going to write NE in this class for Nash equilibrium from now on if for each i so for each player i her choice, so her choice here is si star, that’s i is part of that profile, is a best response, is the best response to the other player’s choices. The other player’s choices. Of course the other player’s choices here are S minus I star. So everyone is playing a best response to everyone else. Alright. Now this is by far the most commonly used solution concepts in game theory.

耶鲁大学博弈论公开课 - 第22集混合策略定义及其在网球比赛中的应用

Thu, 11 Jun 2026 00:09:00 +0800

视频信息

标题: 耶鲁大学博弈论公开课 - 第22集混合策略定义及其在网球比赛中的应用
BV号: BV1u54y1k74g
分集: p22
时长: 73分05秒（4385秒）
作者/来源: 耶鲁大学公开课
原始链接: B站视频
转录方式: Groq Whisper 英文转录；英文在前，中文在后逐段对照。

视频摘要

本集是耶鲁大学博弈论公开课第 22 集，主题为“混合策略定义及其在网球比赛中的应用”。课程以英文课堂讲授和互动讨论为主体，围绕混合策略定义及其在网球比赛中的应用展开，逐步引入博弈论中关于策略、收益、信息、均衡和动态推理的分析框架。本文提供英文原文与中文译文逐段对照，便于跟读、检索和复习。

核心要点

混合策略定义及其在网球比赛中的应用：本集围绕“混合策略定义及其在网球比赛中的应用”展开，是理解后续博弈论模型和课堂案例的基础。
核心概念：讲授重点放在参与者如何根据目标、信息和他人行为选择策略。
课堂案例：课堂通过案例、提问或推导展示抽象模型如何落到具体决策情境。
策略推理：内容强调从结果反推策略条件，训练形式化的战略思维。

点击展开完整转录（73分05秒完整版，中英双语）

视频全文转录（中英双语）

以下为完整中英双语转录，已加标点。英文在前，中文在后，逐段对照。

由 Groq Whisper 转录 → M2.7 B 方案整文标点 + 分段 → M2.7 段号保留翻译 → 逐段对照。

[段 1]

So last time we saw this, we saw an example of a mixed strategy, which was to play a third, a third, a third in our rock, paper, scissors game. All right, and today we’re going to be formal, we’re going to define this. We’re going to define mixed strategies, and we’re going to talk about them, and it’s going to take a while. All right, so let’s start with a formal definition. Definition. A mixed strategy, and I’ll develop notation as I’m going along, so let me call it P-sub-I, I being the person who’s playing it, P-sub-I, is a randomization. It’s a randomization. over I’s pure strategies. All right, so in particular, we’re going to use the notation P-sub-I of S-I to be the probability that player I plays S-I, given that he’s mixing using P-I. All right, so P-I-S-I is the probability that P.I assigns to the pure strategy SI, and to the pure strategy, SI, and to immediately refer that back to our example. So, for example, if I’m playing third, a third, a third, in rock-paper scissors, then P. then P-I is a third, a third, a third, and P-I of rock, that would P-I of R is a third. All right, so without belaboring it, that’s all I’m doing here, is developing some notation. All right? Let’s immediately encounter two things you might have questions about.

耶鲁大学博弈论公开课 on Yagu的小站

耶鲁大学博弈论公开课 - 第1集 导论-五个入门结论

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耶鲁大学博弈论公开课 - 第2集 沉默，信令和苦难教育

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耶鲁大学博弈论公开课 - 第3集 拍卖和获奖者的诅咒

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耶鲁大学博弈论公开课 - 第4集 作弊，惩罚和外包

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耶鲁大学博弈论公开课 - 第5集 战争的消耗

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耶鲁大学博弈论公开课 - 第6集 信息集和子博弈完美

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耶鲁大学博弈论公开课 - 第7集 合作与结局

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耶鲁大学博弈论公开课 - 第8集 落后的感应-国际象棋，战略和可信的威胁

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耶鲁大学博弈论公开课 - 第9集 进化稳定-合作，突变，与平衡

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耶鲁大学博弈论公开课 - 第10集 混合战略棒球，约会和支付您的税

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耶鲁大学博弈论公开课 - 第11集 落后的感应-声誉和决斗

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耶鲁大学博弈论公开课 - 第12集 进化稳定-社会公约，侵略，和周期

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耶鲁大学博弈论公开课 - 第13集 顺序游戏-道德风险，奖励和饥饿的狮子

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耶鲁大学博弈论公开课 - 第14集 落后的感应-承诺，间谍，和先行者优势

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耶鲁大学博弈论公开课 - 第15集 迭代剔除和中位选民定理

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耶鲁大学博弈论公开课 - 第16集 学会换位思考

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耶鲁大学博弈论公开课 - 第1集导论-五个入门结论

耶鲁大学博弈论公开课 - 第2集沉默，信令和苦难教育

耶鲁大学博弈论公开课 - 第3集拍卖和获奖者的诅咒

耶鲁大学博弈论公开课 - 第4集作弊，惩罚和外包

耶鲁大学博弈论公开课 - 第5集战争的消耗

耶鲁大学博弈论公开课 - 第6集信息集和子博弈完美

耶鲁大学博弈论公开课 - 第7集合作与结局

耶鲁大学博弈论公开课 - 第8集落后的感应-国际象棋，战略和可信的威胁

耶鲁大学博弈论公开课 - 第9集进化稳定-合作，突变，与平衡

耶鲁大学博弈论公开课 - 第10集混合战略棒球，约会和支付您的税

耶鲁大学博弈论公开课 - 第11集落后的感应-声誉和决斗

耶鲁大学博弈论公开课 - 第12集进化稳定-社会公约，侵略，和周期

耶鲁大学博弈论公开课 - 第13集顺序游戏-道德风险，奖励和饥饿的狮子

耶鲁大学博弈论公开课 - 第14集落后的感应-承诺，间谍，和先行者优势

耶鲁大学博弈论公开课 - 第15集迭代剔除和中位选民定理

耶鲁大学博弈论公开课 - 第16集学会换位思考

耶鲁大学博弈论公开课 - 第17集足球比赛与商业合作之最佳对策

耶鲁大学博弈论公开课 - 第18集纳什均衡之立场选择、种族隔离与策略随机化

耶鲁大学博弈论公开课 - 第19集纳什均衡之伯川德模型与选民投票

耶鲁大学博弈论公开课 - 第20集纳什均衡之约会游戏与古诺模型

耶鲁大学博弈论公开课 - 第21集纳什均衡之坏风气与银行挤兑

耶鲁大学博弈论公开课 - 第22集混合策略定义及其在网球比赛中的应用