耶鲁大学博弈论公开课

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. ...

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. ...