English With Chinese Translation

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. ...

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. ...

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. ...

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. ...

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. ...

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. ...

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. ...

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. ...

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. ...

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. ...