耶鲁大学公开课博弈论笔记 博弈论 讲

耶鲁大学开放课程博弈论笔记博弈论，是一门研究决策者之间互动行为的学科，它在经济学、政治学、社会学等多个领域发挥着重要作用。

耶鲁大学开放课程中的博弈论课程为我们提供了深入理解和掌握博弈论的机会。

在本篇文章中，我将分享我在学习耶鲁大学开放课程博弈论时所做的笔记和心得体会。

一、博弈论的基本概念和原理1.1 构成博弈论的基本要素博弈论研究的基本要素包括玩家、策略和支付。

玩家是博弈中的决策者，策略是玩家可选择的行动方案，支付是博弈的结果对玩家所产生的效用。

1.2 纳什均衡纳什均衡是博弈论中最重要的概念之一。

在一个博弈中，若每个参与者选择了一个策略，并且没有一个参与者愿意改变自己的策略，那么这种策略组合就被称为纳什均衡。

纳什均衡是一个非合作博弈中的稳定状态。

1.3 合作博弈与非合作博弈博弈论可分为合作博弈和非合作博弈两大类。

合作博弈强调玩家之间的合作与协调，而非合作博弈中玩家之间是相互独立的，没有直接的合作关系。

二、博弈论的应用领域2.1 经济学中的博弈论应用在经济学中，博弈论被广泛应用于市场竞争、拍卖、企业策略等方面。

通过博弈论的模型和方法，我们能够更好地理解各种经济行为和市场现象，并提供决策方案。

2.2 政治学中的博弈论应用政治学中，博弈论主要应用于研究选举、政策制定等政治行为。

博弈论揭示了政治参与者之间的互动关系和利益博弈，为我们分析政治决策提供了一种新的视角。

2.3 社会学中的博弈论应用博弈论在社会学中的应用主要涉及合作与互助、社会规范等方面。

通过博弈论的分析，我们能够更好地理解人类社会中的合作关系、道德行为和社会规范的形成。

三、耶鲁大学开放课程博弈论学习心得在学习耶鲁大学开放课程博弈论的过程中，我深刻体会到博弈论的重要性和应用广泛性。

通过学习博弈论，我不仅了解了博弈论的基本概念和原理，还学会了运用博弈论的方法分析和解决实际问题。

耶鲁大学开放课程博弈论课程的教学内容十分丰富，通过生动的案例分析和实践操作，课程帮助我更好地理解了博弈论的核心思想和应用方法。

耶鲁公开课一博弈论笔记第一节、名词解释优势策略（Dominant strategy ）:不论其他局中人采取什么策略，优势策略对一个局中人而言都是最好的策略。

即某些时候它胜于其他策略，且任何时候都不会比其他策略差。

注：1、"优势策略”的优势是指你的这个策略对你的其他策略占有优势，而不是无论对手采用什么策略，都占有优势的策略。

2、采用优势策略得到的最坏的结果不一定比采用另外一个策略得到的最佳的结果略胜一筹。

严格劣势策略（strictly dominated strategy）:被全面的严格优势策略压住的那个策略，也就是说不是严格优势策略以外的策略。

弱劣势策略：原来不是严格劣势策略，但是经过剔除严格劣势策略后，这个策略就成了严格劣势策略。

例：囚徒困境甲沉默｛合作）甲认罪（背叛乙沉默（合作）二人同服刑半年甲即时获释！乙眼刑F评乙认罪（背扳）甲腮刑10年；乙即时获释二炯服刑2年囚徒到底应该选择哪一项策略，才能将自己个人的刑期缩至最短？两名囚徒由于隔绝监禁，并不知道对方选择；而即使他们能交谈，还是未必能够尽信对方不会反口。

就个人的理性选择而言，检举背叛对方所得刑期，总比沉默要来得低。

试设想困境中两名理性囚徒会如何作出选择：若对方沉默、背叛会让我获释，所以会选择背叛。

若对方背叛指控我，我也要指控对方才能得到较低的刑期，所以也是会选择背叛。

二人面对的情况一样，所以二人的理性思考都会得出相同的结论一一选择背叛。

背叛是两种策略之中的支配性策略。

因此，这场博弈中唯一可能达到的纳什均衡，就是双方参与者都背叛对方，结果二人同样服刑2年。

例：协和谬误20 世纪60 年代，英法两国政府联合投资开发大型超音速客机，即协和飞机。

该种飞机机身大、装饰豪华并且速度快，其开发可以说是一场豪赌，单是设计一个新引擎的成本就可能高达数亿元。

难怪政府也会被牵涉进去，竭力要为本国企业提供更大的支持。

项目开展不久，英法两国政府发现：继续投资开发这样的机型，花费会急剧增加，但这样的设计定位能否适应市场还不知道；但是停止研制也是可怕的，因为以前的投资将付诸东流。

Syllabusby (course_default) — last modified 10-14-2008 04:00 PMDocument Actions•This course is an introduction to game theory and strategic thinking. Ideas such as dominance, backward induction, Nash equilibrium, evolutionary stability, commitment, credibility, asymmetric information, adverse selection, and signaling are discussed and applied to games played in class and to examples drawn from economics, politics, the movies, and elsewhere.ECON 159: Game Theory (Fall, 2007)SyllabusProfessor:Ben Polak, Professor of Economics and Management, Yale University Description:This course is an introduction to game theory and strategic thinking. Ideas such as dominance, backward induction, Nash equilibrium, evolutionary stability, commitment, credibility, asymmetric information, adverse selection, and signaling are discussed and applied to games played in class and to examples drawn from economics, politics, the movies, and elsewhere.Texts:A. Dixit andB. Nalebuff. Thinking Strategically, Norton 1991J. Watson. Strategy: An Introduction to Game Theory, Norton 2002P.K. Dutta. Strategies and Games: Theory And Practice, MIT 1999 Requirements:Who should take this course?This course is an introduction to game theory. Introductory microeconomics (115 or equivalent) is required. Intermediate micro (150/2)is not required, but it is recommended. We will use calculus (mostly one variable) in this course. We will also refer to ideas like probability and expectation. Some may prefer to take the course next academic year once they have more background. Students who have already taken Econ 156b should not enroll in this class.Course Aims and Methods.Game theory is a way of thinking about strategic situations. One aim of the course is to teach you some strategic considerations to take into account making your choices. A second aim is to predict how other people or organizations behave when they are in strategic settings. We will see that these aims are closely related. We will learn new concepts, methods and terminology. A third aim is to apply these tools to settings from economics and from elsewhere. The course will emphasize examples. We will also play several games in class.Outline and Reading.Most of the reading for this course comes from the first ten chapters of Dutta or from the first two parts of Watson. There will be a reading packet for weeks 6-7. The readings are not compulsory, but they will help back up the class material.Grading:Problem sets: 30%Midterm examination: 30%Final examination: 40%Transcript 1 - Introduction: five first lessonsby mvd4 — last modified 09-15-2011 09:34 AMDocument Actions•We introduce Game Theory by playing a game. We organize the game into players, their strategies, and their goals or payoffs; and we learn that we should decide what our goals are before we make choices. With some plausible payoffs, our game is a prisoners' dilemma. We learn that we should never choose a dominated strategy; but that rational play by rational players can lead to bad outcomes. We discuss some prisoners' dilemmas in the real world and some possible real-world remedies. With other plausible payoffs, our game is a coordination problem and has very different outcomes: so different payoffs matter. We often need to think, not only about our own payoffs, but also others' payoffs. We should put ourselves in others' shoes and try to predict what they will do. This is the essence of strategic thinking.Game Theory: Lecture 1 TranscriptSeptember 5, 2007 << backChapter 1. What Is Strategy? [00:00:00]Professor Ben Polak: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 labeled 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 am hoping you can multitask a bit. I'll describe a bit about the class and we'll get a bit of admin under our belts. But please try and lookat--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。

第一课：五个结论1.行为决定结果，但结果不仅取决于你的行为还有别人的行为2.无论别人怎么选，如果选A的结果严格优于B，那么A相对于B是个严格优势策略结论：⑴不要选择严格劣势策略⑵理性的选择使总结果变得更糟即理性选择导致次优结果⑶预先取之，必先知之。

⑷站在别人立场上去分析他们会怎么做？换位思考⑸每个人都是自私的第二课：换位思考博弈的要素有那些：①参与人、②策略和策略集合（1到100）、③一次博弈或策略组合（策略向量或列表即每一个人有一个对应的策略）④收益假设：每个人都知道其他人可能选择的策略，每个人都知道其他人的收益入侵者和防守者矩阵：平坦和崎岖两条路，走崎岖路入侵者损失一个营，两军相遇各损失一个营，。

入侵者防守s—i 表示出来i外其他人每人的策略Ui表示选择i策略的收益。

要先考虑入侵者可能的策略，再选择我应该在哪里防守。

4.参与者i的策略s’i弱劣于其他策略si当且仅当，在对手选择s—i的情况下，参与人i选择si的收益等于和严格优于对手选s_i下他选s’i的收益，U(SI,S_I)＞＝U(S’I,S_I)共同知识：我知道你知道，相互知识并不是共同知识，共同知识是我知道别人所知道的，别人也知道我所知道的。

相互知识是我不知道别人心里知道的。

游戏2：选数字，不让其他人看到，谁最接近全班的平均数的三分之二，谁就是赢家。

奖金是5美元减去所选数与平均数的三分之二之差的百分数。

游戏总结：.如果是随即选择的话平均数大概是50 ①选择大于67的人，是非理性的，因为他们选择了劣势策略。

②选择45与67之间的人，认为其他人全是傻子。

③经过反复换位，最终选择1.④然而选择1并不是赢家，因为并不是所有人都是理性的。

第三课迭代剔除劣势策略博弈时对方有多老练还要考虑到对方认为我有多老练，即迭代剔除劣势策略：站在对方的立场考虑对方会怎么做，也要考虑对方会站在你的角度考虑你会怎么做中间选民定理可以左右政策的制定肯尼迪和尼克松。

这个政治性模型的缺点是：现实生活中选民并不是按10%均匀分布的；并非人人都投票，有弃权票；并非两个候选人；候选人未必坚守自己的立场或者选民未必相信候选人的立场。

第一讲导论—五个入门结论1。

通过成绩博弈模型可以知道，不选择严格劣势策略，因为每次博弈会得到更好的收益.2。

通过囚徒的困境博弈模型可以知道，理性选择导致次优的结果（协商难以达成目的的原因不是因为缺少沟通，而是没有强制力）。

3。

通过愤怒天使博弈模型可以知道，汝欲得之,必先知之；永远选择优势策略，选择非劣势策略，损失小，如果对手有优势策略则应以此作为选择策略的指导.4.如果想要赢，就应该站在别人的立场去分析他们会怎么做.第二讲学会换位思考1.构成博弈要素包括，参与人,参与人的策略以及收益.2。

所谓严格优势策略，就是指不论对方采取什么策略，采取的这个策略总比采取其他任何策略都好的策略。

3。

在博弈中剔出某些选择时需要站在别人的角度去思考结果,因为对手不会选择劣势策略；同时要考虑到对手也是一个理性的参与人。

4.在博弈中剔除某些选择是一种直接思考，同时也是作为一个理性参与人的选择。

第三讲迭代剔除和中位选民定理1。

在选民投票博弈模型中,通过不断地迭代以及剔除来决定策略，由此,我们得到了一种新的选择策略的方法：迭代剔除法。

2.选民投票博弈模型的结果与现实存在偏差，主要是因为：现实中选民并不是均匀分布的;选民通常根据候选人的性格而非政治立场来进行投票，而政治立场只是单一维度；只适用于只有两个候选人的情况;④同时存在弃权票；⑤选民未必相信候选人所声明的立场。

3.建立模型，是为了更好的描述事实以激发灵感，模型是有重要的事是抽象而来，逐步增加约束条件完善模型观察结果，比较分析结果的变化。

第四节足球比赛与商业合作之最佳对策1。

点球博弈模型告诉我们，不要选择一个在任何情况或信念下都不是最佳对策的策略。

2.最佳对策：参与人针对对手策略的定义：参与人i的策略s^i（简写成BR）是对手策略S—i的最佳对策，如果参与人i在对手的策略S-i下选S^i的收益弱优于其它对策Si`，这对参与人i的所有Si`都适用，则策略S^i是其它参与人策略S—i的最佳对策。

So this is Game Theory Economics 159.欢迎来到经济学159 博弈论If you're here for art history,如果你是来上艺术史的you're either in the wrong room or stay anyway,那你走错教室了不过你不妨留下来maybe this is the right room; but this is Game Theory, okay.没准你会喜欢这门课这里是博弈论You should have four handouts; everyone should have four handouts.你们每人都应该有四页讲义人手一份There is a legal release form--里面有一授权书we'll talk about it in a minute--about the videoing.是关于视频采集的我们一会再说这个There is a syllabus, which is a preliminary, it's also online.有一初步教学大纲上也有And there are two games labeled Game 1 and Game 2.有两页分别印有游戏1和游戏2的传单Can I get you all to look at Game 1 and start thinking about it.大家先浏览下游戏1 然后思考一下And while you're thinking about it, i am hoping you can multitask a bit. 你们一边思考一边听我说I'll describe a bit about the class我来简单介绍下这门课程and we'll get a bit of admin under our belts.还有这门课程的评分细则But please try and look at--somebody's not looking at it,请大家看下游戏1 我知道有人没看because they're using it as a fan here--他们用那纸扇风呢So look at Game 1 and fill out that form for me, okay?快浏览下游戏1 然后填完好吗So while you're filling that out, let me tell you a little你们一边写一边听我说bit about what we're going to be doing here.我来简单地介绍一下这门课So what is Game Theory?什么是博弈论Game Theory is a method of studying strategic situations.博弈论研究策略形势So what's a strategic situation?那什么是策略形势呢Well let's start off with what's not a strategic situation.我们先看看什么不属于策略形势In your Economics - in your Intro Economics class in 115 or 110,在你们经济学基础课115或者110中you saw some pretty good examples of situations that were not strategic. 应该讲过一些不是策略形势的案例You saw firms working in perfect competition.比如说自由竞争企业Firms in perfect competition are price takers:这些企业是价格承受者they don't particularly have to worry about他们不必担心the actions of their competitors.他们的竞争对手的策略You also saw firms that were monopolists又比如说垄断企业and monopolists don't have any competitors to worry about,垄断企业没有竞争对手so that's not a particularly strategic situation.所以这也不是策略形势They're not price takers but they take the demand curve.他们不是价格承受者但面对需求曲线Is this looking familiar for some of you who can remember对于你们这些学过经济学115的来说doing 115 last year or maybe two years ago for some of you?这些听起来都不陌生吧Everything in between is strategic.介于这两种情况之间的就是策略形势So everything that constitutes imperfect competition也就是说不完全竞争的情况is a strategic setting.就是策略形势Think about the motor industry, the motor car industry.比如汽车产业在汽车产业里Ford has to worry about what GM is doing and what Toyota is doing,福特关注通用和丰田的决策and for the moment at least现在可能暂时what Chrysler is doing but perhaps not for long.还得关注克莱斯勒的决策So there's a small number of firms and their actions affect each other. 少数几家公司的决策会互相影响So for a literal definition of what strategic means:策略形势书面定义是it's a setting where the outcomes that affect you depend on actions, 行为影响结果然而结果不仅not just on your own actions, but on actions of others.取决于你的行为还取决于其他人的行为All right, that's as much as I'm going to say for preview right now. 好了暂时就先介绍这么多We're going to come back and see plenty of this通过学习本学期的课程over the course of the next semester.你们会接触更多类似案例So what I want to do is get on to where this applies.下面我们讲讲博弈论适用于什么领域It obviously applies in Economics, but it also applies in politics, 显然适用于经济学但也适用于政治学and in fact, this class will count as a Political Science class实际上对政治专业的同学来说if you're a Political Science major.它也算作政治课You should go check with the DUS in Political Science. It counts.回去咨询下本科教学主管确实算的Game Theory is very important in law these days.近年来博弈论在法学上也举足轻重So for those of you--for the half of you我估计你们多数人可能会去读法学院--that are going to end up in law school, this is pretty good training. 博弈论对你们来说是门不错的基础课Game Theory is also used in biology博弈论同样适用于生物学and towards the middle of the semester在本学期期中的时候we're actually going to see some examples of我们会探讨一下Game Theory as applied to evolution.博弈论应用于生物进化论的案例And not surprisingly, Game Theory applies to sport.而且毫不奇怪博弈论适用于体育So let's talk about a bit of admin.我们接下来谈谈评分标准How are you doing on filling out those games?这两个游戏你们填好了没有Everyone managing to multitask.每个人都要学会一心多用啊Filling in Game 1? Keep writing.还在填游戏1 好吧继续填I want to get some admin out of the way我们继续讲评分标准and I want to start by getting out of the way不过我得先介绍一下what is obviously the elephant in the room.教室里的大家伙Some of you will have noticed that there's a camera crew here, okay. 有些人注意到了这几位摄像人员So as some of you probably know,可能你们已经知道了Yale is undergoing an open education project耶鲁大学正在开展一个教育项目and they're videoing several classes,我们在录制一些课程的录像and the idea of this,这样做的目的是让is to make educational materials available beyond the walls of Yale. 耶鲁外的人也能享受到这些教学资源In fact, on the web, internationally,课程将被发布到网络上so people in places, maybe places in the U.S.全球各地的人都能看到比如美国人or places miles away, maybe in Timbuktu or whatever,或者更遥远的国度像廷巴克图who find it difficult to get educational materials他们可能在当地大学from the local university or whatever,不容易得到这样的教育资源can watch certain lectures from Yale on the web.他们就可以到耶鲁观看这些视频Some of you would have been in classes that do that before.有些同学可能之前参加过这种课程What's going to different about this class is that这门课的不同之处在于you're going to be participating in it.大家都要参与到课程中来The way we teach this class is we're going to play games,课堂上我们通过做游戏来博弈we're going to have discussions, we're going to talk among the class, 课上会有随堂讨论课堂交流and you're going to be learning from each other,我们相互学习这样看视频的学生and I want you to help people watching at home to be able to learn too. 也能收到良好的教学效果And that means you're going to be on film, at the very least on mike. 但同时这意味着你要被拍到视频中来So how's that going to work?至少也会被录音课程怎么拍摄呢Around the room are three T.A.S holding mikes.教室里有三位助教持有麦克风Let me show you where they are: one here, one here, and one here.我来告诉大家助教坐在哪里When I ask for classroom discussions,当我们进行随堂讨论时I'm going to have one of the T.A.S go to you with a microphone我会请一位助教拿着麦克风到你那much like in "Donahue" Or something. Okay.就想多纳休那样At certain times, you're going to be seen on film,有时候你会被拍摄到so the camera is actually going to come around and point in your direction. 此时摄像机会转到你所在的方向Now I really want this to happen.我希望大家多多配合I had to argue for this to happen, cause I really feel that我来解释一下我的理由我觉得this class isn't about me.这门课不应该仅仅由我来讲I'm part of the class obviously,没错我是课程的一部分but it's about you teaching each other and participating.但你们也要参与到课堂中来But there's a catch, the catch is,但是这会有个条件that that means you have to sign that legal release form.你们都要签署授权书So you'll see that you have in front of you a legal release form,你们的面前应该有授权书you have to be able to sign it, and what that says is that授权书的大概容是we can use you being shown in class.允许我们把你拍摄进来Think of this as a bad hair day release form.大家考虑好日后你要是在视频里All right, you can't sue Yale later if you had a bad hair day.发现你糟糕的发型可别起诉耶鲁大学For those of you who are on the run from the FBI,被FBI通缉的签证失效的your Visa has run out, or you're sitting next to your ex-girlfriend, 还有前女友就坐在旁边的now would be a good time to put a paper bag over your head.赶快找个纸袋子把脸给蒙上All right, now just to get you used to the idea,还要说一下每节课我们都会in every class we're going to have I think the same two people,看到这两名工作人员so Jude is the cameraman; why don't you all wave to Jude.裘德是摄影师大家跟裘德打个招呼This is Jude okay. And Wes is our audio guy: this is Wes.这位就是裘德韦斯是录音师And I will try and remember not to我会尽量注意include Jude and Wes in the classroom discussions,不要让他们两位加入课堂讨论的but you should be aware that they're there.但是你们也要注意到他们的存在Now, if this is making you nervous,要是这令你很紧if it's any consolation, it's making me very nervous.它会让我更紧这权当安慰了吧So, all right, we'll try and make this class我会尽量让work as smoothly as we can, allowing for this extra thing.课堂顺利地进行下去还有一件事Let me just say, no one's making any money off this--让我说完没有人会从中得到好处at least I'm hoping these guys are being paid--虽然我也希望他们会得到酬劳but me and the T.A.S are not being paid.但至少我和助教们是没有酬劳的The aim of this, that I think is a good aim, it's an educational project, 这完全出于好意这是个教育项目and I'm hoping you'll help us with it.我也希望你们也能尽己所能把它做好The one difference it is going to mean, is that还有希望大家都能相互理解一下at times I might hold some of the discussions for the class,当我们举行课堂讨论的时候coming down into this part of the room, here,请你们靠前站出来一点to make it a little easier for Jude.这样便于裘德拍摄All right, how are we doing now on filling out those forms?言归正传你们填好了没Has everyone filled in their strategy for the first game?各位是否都填好第一个游戏了Not yet. Okay, let's go on doing a bit more admin.还没有那我们多介绍下评分标准The thing you mostly care about i'm guessing, is the grades.我猜你们最关心的应该是成绩了All right, so how is the grade going to work for this class?那么这门课是怎么评分的呢30% of the class will be on problem sets,课堂作业占总分数的30%30% of the grade; 30% on the mid-term,期中考试占30%and 40% on the final; so 30/30/40.期末考试占40% 即30/30/40The mid-term will be held in class on October 17;期中考试在十月十七日that is also in your syllabus.教学大纲上也写了Please don't anybody tell me late -所以以后千万别跟我说any time after today you didn't know when the mid-term你不知道什么时候期中考试was and therefore it clashes with 17 different things.然后还在考试那天安排大一堆事儿去做The mid-term is on October 17, which is a Wednesday, in class.期中考试在十月十七号周三随堂举行All right, the problem sets:关于课堂作业there will be roughly ten problem sets我应该会安排十次左右的课堂作业and I'll talk about them more later on when I hand them out.在留作业的时候我再细说The first one will go out on Monday but it will be due ten days later. 周一留第一份作业十天之交上来Roughly speaking they'll be every week.差不多每周都有课堂作业The grade distribution:有关分数的分布all right, so this is the rough grade distribution.我介绍下大体的分数的分布Roughly speaking, a sixth of the class are going to end up with A's, 总体来说六分之一的人会得到Aa sixth are going to end up with A-,六分之一的人会得到A-a sixth are going to end up with B+,六分之一的人会得到B+a sixth are going to end up with B,六分之一的人会得到Ba sixth are going to end up with B-,六分之一的人会得到B-and the remaining sixth, if I added that up right,剩下的六分之一如果我没算错are going to end up with what I guess we're now calling这些人将会得到the presidential grade, is that right?传说中的"超优"成绩That's not literally true. I'm going to squeeze it a bit,但我可能稍微压缩下分数段I'm going to curve it a bit,我会让分数段更有弹性so actually slightly fewer than a sixth will get straight A's,实际上略少于六分之一的人会得到Aand fewer than a sixth will get C's and below.略少于六分之一会得到CWe'll squeeze the middle to make them be more B's.我们这样压缩会使更多的人得到BOne thing I can guarantee from past experience in this class,不过从教学经验看is that the median grade will be a B+.中间成绩应该是B+The median will fall somewhere in the B+'s.分数中位数会在B+的附近Just as forewarning for people who have forgotten what a median is, 稍微提示下忘记中位数含义的同学that means half of you--not approximately half,这也就是说不是一半左右it means exactly half of you--是绝对一半的同学will be getting something like B+ and below会得到B+的成绩或更低的成绩and half will get something like B+ and above.另一半会到B+的成绩或更高的成绩Now, how are you doing in filling in the forms?那两表你们填得怎么样了Everyone filled them in yet?每个人都填好了吗Surely must be pretty close to getting everyone filled in.应该差不多每个人都填好了吧All right, so last things to talk about在我把表收回之前before I actually collect them in - textbooks.我再讲最后一件事课本There are textbooks for this class.这门课的课本The main textbook is this one, Dutta's book Strategy and Games.主要是这本杜塔的《策略与博弈》If you want a slightly tougher book, more rigorous book,要是你想要一本更难更有挑战的try Joel Watson's book, Strategies.试试乔尔?沃森的《策略》Both of those books are available at the bookstore.这两本书在书店都有卖的But I want to warn everybody ahead of time,不过我先提个醒I will not be following the textbook.我不会完全参照课本I regard these books as safety nets.课本只不过是救命稻草If you don't understand something that happened in class,要是你课堂上没听懂you want to reinforce an idea that came up in class,或者你课下想深入了解下课上的容then you should read the relevant chapters in the book你应该去读书上对应的章节and the syllabus will tell you which chapters to read for each class, 教学大纲会告诉你每堂课讲哪章or for each week of class, all right.或者每周讲哪几章But I will not be following these books religiously at all.但是我不会严格按照课本来讲课In fact, they're just there as back up.重申一下课本就是救命稻草In addition, I strongly recommend people read Thinking Strategically. 对了我强烈建议读一读《战略思想》This is good bedtime reading. Do any of you suffer from insomnia?这是本不错的睡前读物你们失眠吗It's very good bedtime reading if you suffer from insomnia.你要是失眠它绝对是最好的睡前读物It's a good book and what's more这也的确是本好书there's going to be a new edition of this book this year而且今年会有新版上市and Norton have allowed us to get advance copies of it.出版商会让我们提前得到新版的So if you don't buy this book this week,如果你这周不买I may be able to make the advance copy of the new可能下周你们edition available for some of you next week.就能买到新版的了I'm not taking a cut on that either, all right,我不会从中得到提成there's no money changing hands.这不是推销All right, sections are on the syllabus sign up小组讨论的安排在教学大纲上sorry on the website, sign up as usual.哦我说错了像平常一样在网上注册Put yourself down on the wait list如果你想换个小组if you don't get into the section you want.请在等候名录里预约You probably will get into the section you want once we're done.一般你只需要预约一次就可以了All right, now we must be done with the forms.你们现在应该填完了吧Are we done with the forms?都填完了吗All right, so why don't we send the T.A.S, with or without mikes,我们把表交给助教吧up and down the aisles and collect in your Game #1;让他们来帮我收一下游戏1not Game #2, just Game #1.不要游戏2 只要游戏1Just while we're doing that, I think the reputation of this class-- 收表的时候我来说说这门课的名声I think--if you look at the course evaluations online or whatever,你们要是在上看了教学评估is that this class is reasonably hard but reasonably fun.就会发现这门课有点难但也很有趣So I'm hoping that's what the reputation of the class is.我也希望这门课是这样的If you think this class is going to be easy,你要是认为这门课挺简单I think it isn't actually an easy class. It's actually quite a hard class, 这不是轻松的课事实上它有点难but I think I can guarantee it's going to be a fun class.我保证这门课一定很有趣Now one reason it's a fun class,为什么这门课很有趣is the nice thing about teaching Game Theory因为学习博弈论- quieten down folks--大家安静一下one thing about teaching Game Theory is, you get to play games,在课堂上我们通过一些游戏来学习博弈and that's exactly what we've just been doing now.我们不刚做完一个游戏吗This is our first game and we're going to play games throughout the course, 这是第一游戏整个课程充满了游戏sometimes several times a week, sometimes just once a week.有时候一周做几次有时一周一次We got all these things in?表收齐了吗Everyone handed them in?每个人都交了吧So I need to get those counted.下面要开始统计了Has anyone taken the Yale Accounting class?有人上过会计课吗No one wants to - has aspirations to be - one person has.有人想帮忙统计吗这有一个人想I'll have a T.A. do it, it's all right, we'll have a T.A. do it.我还是安排助教做吧So Kaj, can you count those for me? Is that right?卡茄你帮我统计一下好吗Let me read out the game you've just played.我们回顾一下刚才进行的游戏"Game 1, a simple grade scheme for the class."游戏1是一个简单的成绩博弈Read the following carefully.请仔细阅读以下条款Without showing your neighbor what you are doing,在不被你同桌看到的情况下put it in the box below either the letter Alpha or the letter Beta. 在方框中填写字母α或者字母βThink of this as a grade bid.把这看成成绩的赌注I will randomly pair your form with another form我会随机把你们分成两两一组and neither you nor your pair will ever know with whom you were paired. 你们不知道会跟谁分到一组Here's how the grades may be assigned for the class.按如下方法给出你们的成绩Well they won't be,纯属娱乐大家别当真If you put Alpha and you're paired with Beta,如果你选α而你对手选βthen you will get an A and your pair a C.那么你得A你对手得CIf you and your pair both put Alpha, you'll both get B-.如果你们都选α 那么你们都得B-If you put Beta and you're paired with Alpha,如果你选β你对手选αyou'll get a C and your pair an A.你得C你对手得AIf you and your pair both put Beta, then you'll both get B+."如果你们都选β 你们都得B+"So that's the thing you just filled in.这就是你们之前填的东西Now before we talk about this,在我们讨论之前let's just collect this information in a more useful way.先有效地整理一下这些信息So I'm going to remove this for now.我先把它们擦掉We'll discuss this in a second,一会再开始分析but why don't we actually record what the game is, that we're playing first.我们先记录一下这个游戏的容So this is our grade game, and what I'm going to do,就是我们的成绩博弈since it's kind of hard to absorb all the information因为这么长一段文字just by reading a paragraph of text,从中摘取信息有点困难I'm going to make a table to record the information.不如我们列表整理信息So what I'm going to do is I'm going to put me here,那么我把我写在这里and my pair, the person I'm randomly paired with here,我对手就是被随机分到的人写在这and Alpha and Beta, which are the choices I'm going to make here还有是α和β 就是我要做的选择and on the columns Alpha and Beta, the choices my pair is making.还有我对手要做的选择In this table, I'm going to put my grades.我把我的成绩填到表格里So my grade if we both put Alpha is B-, if we both put Beta, was B+. 如果我们都选α我得B- 都选β我得B+If I put Alpha and she put a Beta, I got an A,如果我选α她选β 我得Aand if I put Beta and she put an Alpha, I got a C.如果我选β她选α 那么我得CIs that correct? That's more or less right?这些都对吧Yeah, okay while we're here, why don't we do the same for my pair?好了我们再把对手的情况也写下来So this is my grades on the left hand table,我的成绩写在左边的表格里but now let's look at what my pair will do, what my pair will get.我们再看看我对手她会得到什么成绩So I should warn the people sitting at the back提醒一下坐在后面的人that my handwriting is pretty bad, that's one reason for moving forward. 我的板书写得很糟所以最好往前坐The other thing I should apologize at this stage of the class is my accent. 还有我得检讨的是我的口音I will try and improve the handwriting,我会努力写好板书there's not much I can do about the accent at this stage.但是口音暂时不太好改So once again if you both put Alpha then my pair gets a B-.如果我们都选α 我对手得B-If we both put Beta, then we both get a B+;如果我们都选β 我们都会得到B+in particular, my pair gets a B+.此情况下我对手得B+If I put Alpha and my pair puts Beta, then she gets a C.如果我选α我对手选β 那么她得CAnd if I put Beta and she puts Alpha, then she gets an A.如果我选β她选α 那么她得ASo I now have all the information由此我就把这纸上的that was on the sheet of paper that you just handed in.所有信息都包含进来了Now there's another way of organizing this that's standard in Game Theory,下面再用博弈论的标准方式来整理信息so we may as well get used to it now on the first day.从今天以后大家要习惯用这种标准Rather then drawing two different tables like this,与其画两个不同的表格what I'm going to do is I'm going to take the second table不如把第二个表格的容插入到and super-impose it on top of the first table.第一个表中Okay, so let me do that and you'll see what I mean.我来做个示你就明白我的意思了What I'm gonna do is draw a larger table, the same basic structure: 我要画个结构相同的大表格I'm choosing Alpha and Beta on the rows,用列来表示我选α还是βmy pair is choosing Alpha and Beta on the columns,用行来表示我对手选α还是βbut now I'm going to put both grades in.但我要把两人成绩写在一个单元格里So the easy ones are on the diagonal:这样就更直观了you both get B- if we both choose Alpha;如果我们都选α的话得B-we both get B+ if we both choose Beta.如果我们都选β的话得B+But if I choose Alpha and my pair chooses Beta,要是我选α我对手选βI get an A and she gets a C.我得A 她得CAnd if I choose Beta and she chooses Alpha,如果我选β她选αthen it's me who gets the C and it's her who gets the A.我得C而她得ASo notice what I did here.注意下我的表示方法The first grade corresponds to the row player, me in this case,单元格第一个成绩是我的成绩and the second grade in each box corresponds to the column player, 每个单元格第二个成绩是my pair in this case.我对手的成绩So this is a nice succinct way of这样就把前两表格的信息recording what was in the previous two tables.更简明地表述出来了This is an outcome matrix; this tells us everything that was in the game. 它是一个列出了博弈所有容的矩阵Okay, so now seems a good time to start talking about what people did. 现在我们来考虑一下我们的选择So let's just have a show of hands.我们举手表决吧How many of you chose Alpha?多少人选了α?Leave your hands up so that Jude can catch that,先不要放下手让裘德拍一下so people can see at home, okay.这样看视频的人也能看到All right and how many of you chose Beta?多少人选了β?There's far more Alphas - wave your hands the Beta's okay.远远少于选α的先不要放下手All right, there's a Beta here, okay.这里有一个选β的So it looks like a lot of - well we're going to find out,我们来数一下确认一下we're going to count--but a lot more Alpha's than Beta's.选α的人要远远多于选βLet me try and find out some reasons why people chose.我们来探讨下你们为什么这么选So let me have the Alpha's up again.来看看都谁选α了So, the woman who's in red here,穿红色衣服的女士can we get a mike to the -yeah, is it okay if we ask you?递给她一个麦克风You're not on the run from the FBI? We can ask you why?请问没被FBI通缉吧?Okay, so you chose Alpha right? So why did you choose Alpha?你选了α对吧你为什么要选α呢Realized that my partner chose alpha, therefore I chose .我感觉我对手会选α因此我也选αAll right, so you wrote out these squares,这么说你也写下了这些矩阵you realized what your partner was going to do, and responded to that. 你分析出了对手的选择并依此做出的选择Any other reasons for choosing Alpha around the room?还有别的原因使你们选α吗Can we get the woman here?把麦克风递给那位女士好吗Try not to be intimidated by these microphones,它们只不过是麦克风而已they're just mikes. It's okay.别紧The reason I chose Alpha, regardless of what my partner chose,我选α是因为不管我对手选什么I think there would be better outcomes than choosing Beta.我选α得到的成绩总会比选β的要好All right, so let me ask your names for a second-so your name was?请问你叫什么名字?Courtney.考特尼Courtney and your name was?考特尼另一位女士的名字是Clara Elise.克莱拉?埃莉斯So slightly different reasons, same choice Alpha.虽然原因不尽相同但她们都选了αClara Elise's reason - what did Clara Elise say?克莱拉?埃莉斯的理由是她怎么说She said, no matter what the other person does,她说无论别人怎么选she reckons she'd get a better grade if she chose Alpha.她觉得选α会使自己得到最优的结果So hold that thought a second, we'll come back to先保留这个说法我们稍后再做讨论is it Clara Elise, is that right?这是克莱拉?埃莉斯的理由We'll come back to Clara Elise in a second.我们一会再讨论这个理由Let's talk to the Beta's a second;我们先来讨论一下选β的理由let me just emphasize at this stage there are no wrong answers.我要强调一下这里没有错误的答案Later on in the class there'll be some questions that have wrong answers. 在以后在课上可能会有错误的答案Right now there's no wrong answers.但是现在没有错误的答案There may be bad reasons but there's no wrong answers.有不充分的理由但没有错误的理由So let's have the Beta's up again. Let's see the Beta's.请选β的再举下手看看有谁选了βOh come on! There was a Beta right here.之前这里有选β的啊You were a Beta right? You backed off the Beta, okay.你选过β对吗? 哦你改变主意了So how can I get a mike into a Beta?能不能把麦克风给一位选了β的同学Let' s stick in this aisle a bit.我们往过道这边来一点Is that a Beta right there? Are you a Beta right there?那有人选β对吗你是不是选了βCan I get the Beta in here? Who was the Beta in here?这边有人选β的吗Can we get the mike in there? Is that possible?能把麦克拿到那里吗In here - you can leave your hand so that - there we go.这有一个选β的先别放下手对了Just point towards - that's fine, just speak into it, that's fine. 把麦克对着他请讲So the reason right?为什么选β对吗Yeah, go ahead.没错继续说I personally don't like swings that much我不喜欢成绩波动很大的and it's the B-/B+ range,比如B-/B+这个围so I'd much rather prefer that to a swing from A to C,所以我还是喜欢像A到C这样小点的and that's my reason.这就是我的原因All right, so you're saying it compresses the range.你说的意思是压缩围I'm not sure it does compress the range.但是我不太确定这是否压缩了围I mean if you chose Alpha, you're swinging from A to B-;要是你选α 你的分数会在A到B-and from Beta, swinging from B+ to C.选β 分数围会在B+到CI mean those are similar kind of ranges这两个围大小差不多but it certainly is a reason.但这也算是个原因Other reasons for choosing?还有别的原因吗Yeah, the guy in blue here, yep, good.。

耶鲁大学公开课博弈论观后感《耶鲁大学公开课博弈论观后感》耶鲁大学公开课是一门引人入胜的课程，给我们带来了诸多关于博弈论的深刻思考。

博弈论作为一门重要的数学分支，在现代社会中扮演着越来越重要的角色。

通过参与这门公开课，我深刻认识到博弈论的实际应用和其在解决现实问题中的重要性。

下面是我对耶鲁大学公开课博弈论的观后感。

博弈论是由经济学家约翰·冯诺伊曼和数学家奥斯卡·摩根斯坦于20世纪40年代提出的一门数学分支。

博弈论研究的是决策者在不同环境下的最佳策略选择，以及他们之间相互影响的策略关系和收益情况。

通过博弈论，我们可以研究个体在策略选择时面临的困境和冲突，以及如何通过分析对手的策略来制定自己的决策，从而达到最大化自身利益的目标。

在耶鲁大学公开课中，我学到了很多博弈论的基本概念和方法。

课程将博弈论应用到了不同的领域，包括经济学、政治学和生物学等等，展示了博弈论在解决实际问题中的广泛应用。

通过学习这些案例，我深刻认识到博弈论在现代社会中的重要性和必要性。

在博弈论中，最基本的概念之一是“囚徒困境”。

囚徒困境是一种典型的博弈情景，其中两个犯人面临选择合作或背叛的问题。

如果两个犯人都选择合作，则能够达成最好的结果；然而，如果两个犯人都选择背叛，则会导致最坏的结果。

这个案例反映了个体利益和整体利益之间的矛盾，以及自利和合作之间的冲突。

通过分析囚徒困境，我们可以理解为什么在某些情况下，即使两个个体都知道通过合作可以达到更好的结果，但他们仍然选择背叛对方。

除了囚徒困境，课程还介绍了其他一些经典的博弈情景，如“霍布森选房问题”和“拍卖博弈”。

这些案例展示了博弈论在经济决策中的应用。

在霍布森选房问题中，一个房东面临租给两个不同租客的选择。

如果房东选择错了客户，那么他将空置房子并输掉租金收入。

而在拍卖博弈中，各个买家根据自己的估值参与竞价，最终高出其他人的价位的买家将赢得拍卖物品。

这些案例让我深刻认识到个体决策如何受到其他参与者的策略选择的影响，并且如何通过分析和预测其他参与者的行为来制定最佳策略。

博弈论的读书笔记博弈论，这一充满智慧和策略的领域，如同一个神秘的棋局，每一步决策都可能影响最终的胜负。

通过对相关书籍的研读，我仿佛走进了一个充满谋略与思考的世界。

博弈论研究的是在互动情境中，参与者如何做出最优决策。

这里的“最优”并非单纯的自身利益最大化，而是在考虑其他参与者行动的基础上，寻求相对最优的结果。

让我们从一个简单的例子说起——“囚徒困境”。

两个犯罪嫌疑人被分别审讯，如果两人都保持沉默，那么每人判刑一年；如果一人坦白而另一人沉默，坦白者将被释放，沉默者判刑十年；如果两人都坦白，则每人判刑五年。

在这种情况下，从个体角度看，坦白似乎是最优选择，因为无论对方如何选择，坦白都能带来相对较轻的刑罚。

但如果两人都这样想，最终的结果却是两人都判刑五年，这并非整体的最优结果。

这个例子深刻地揭示了个体理性与集体理性之间的冲突。

在现实生活中，类似的情况屡见不鲜。

比如企业之间的价格战，每家企业都想通过降低价格来吸引更多客户，获取更大的市场份额。

但当所有企业都这样做时，整个行业的利润都会下降，大家都受到损失。

博弈论中的另一个重要概念是“纳什均衡”。

以“斗鸡博弈”为例，两个司机相向而行，如果都不让路，就会发生碰撞，双方都受损；如果一方让路，让路的一方会觉得丢面子，不让路的一方则会顺利通过。

在这个博弈中，存在两个纳什均衡，即一方让路，另一方不让路。

这种均衡状态一旦达到，任何一方单方面改变策略都不会使其受益。

在博弈中，信息的掌握程度也至关重要。

如果一方拥有更多或更准确的信息，就可能在博弈中占据优势。

比如在拍卖中，知道其他竞拍者的心理价位和出价策略，就能更好地决定自己的出价。

同时，博弈的类型也多种多样。

有完全信息静态博弈、完全信息动态博弈、不完全信息静态博弈和不完全信息动态博弈。

每种类型都有其独特的特点和分析方法。

完全信息静态博弈中，参与者同时做出决策，且对彼此的策略和收益都了如指掌。

而完全信息动态博弈则是参与者依次做出决策，后面的参与者能够看到前面参与者的决策。

博弈论读书笔记博弈论，听起来似乎是一个高深莫测的概念，但实际上，它在我们的日常生活中无处不在。

从下棋打牌到商业竞争，从人际关系处理到国家之间的政治博弈，都有着博弈论的影子。

博弈论的核心在于研究决策主体在相互作用时的决策以及这种决策的均衡问题。

简单来说，就是当我们在做决策时，需要考虑到其他人可能的反应和决策，而其他人也在同样考虑着我们的可能行动，这就形成了一种相互影响的局面。

比如在玩石头剪刀布的游戏中，我们的选择并不是随意的。

如果我们一直出石头，对手很可能会猜到并且出布来克制我们。

所以我们需要不断地变换策略，试图猜测对手的想法，同时防止自己的想法被对手轻易识破。

这虽然只是一个简单的小游戏，但已经体现了博弈论的基本思想。

再来看一个商业中的例子。

假设市场上有两家竞争的公司 A 和 B，都在考虑是否要降低产品价格来吸引更多的客户。

如果 A 公司降价，而 B 公司不降价，那么 A 公司可能会获得更多的市场份额；但如果 B公司也降价，那么两家公司的利润可能都会受到影响。

在这种情况下，A 公司在做决策时就必须考虑 B 公司的可能反应，反之亦然。

这就是一种典型的商业博弈。

博弈论中有几个重要的概念。

一个是“纳什均衡”，指的是一种策略组合，在这种组合中，每个参与者的策略都是对其他参与者策略的最优反应。

也就是说，在纳什均衡状态下，任何一个参与者如果单方面改变自己的策略，都不会得到更好的结果。

另一个重要概念是“占优策略”。

如果对于某个参与者来说，无论其他参与者选择什么策略，某一种策略对他来说始终是最优的，那么这种策略就是占优策略。

博弈的类型也多种多样。

有“零和博弈”，在这种博弈中，一方的收益必然等于另一方的损失，总和为零。

比如赌博就是一种典型的零和博弈。

还有“非零和博弈”，在这种博弈中，各方的收益和损失之和不为零，可能是正和，也可能是负和。

在日常生活中，我们也经常会遇到各种各样的博弈场景。

比如在和朋友分配任务时，如何分配才能让大家都满意，同时保证任务能够高效完成，这就是一种博弈。

中文名: 耶鲁大学开放课程：博弈论英文名: Open Yale course：Game Theory版本: 更新完毕[MOV]发行时间: 2009年地区: 美国对白语言: 英语文字语言: 英文简介:课程类型：经济课程介绍：这门课程是系统介绍有关博弈论和战略思想。

比如支配思想、落后的感应、纳什均衡、进化稳定性、承诺，信誉，信息不对称，逆向选择等。

并在课堂上提供了各种游戏以及经济、政治，电影和其他方面的案例来讨论。

关于课程主讲人：Ben Polak教授任职于耶鲁大学管理学院经济系。

他在剑桥大学Trinity College 获得学士学位，在西北大学获得硕士学位，在哈佛大学获得博士学位。

他是微观经济理论和经济史方面的专家。

他的论文在Economic Letters、Journal of Economic Theory、Journal of Economic History、Journal of Legal Studies、Journal of Theoretical and Institutional Economics、Econometrica等学术期刊多次发表。

他最近的研究是“广义功利主义和海萨尼的公正观察员定理”和“平均分散的偏好”课程结构：本耶鲁大学课程每周在学校上两次课，每次75分钟，2007年秋季拍摄作为耶鲁大学开放课程之一。

课程视频截图：课程安排：1 Introduction: five first lessons 简介：五年前的教训2 Putting yourselves into other people's shoes 设身处地为他人着想3 Iterative deletion and the median-voter theorem 迭代删除和位数选民定理4 Best responses in soccer and business partnerships 最佳反应在足球和商业伙伴关系5 Nash equilibrium: bad fashion and bank runs 纳什均衡：坏时尚及银行挤兑6 Nash equilibrium: dating and Cournot 什均衡：约会和诺7 Nash equilibrium: shopping, standing and voting on a line 纳什均衡：购物，并参加表决的常委会上线8 Nash equilibrium: location, segregation and randomization 纳什均衡：定位，隔离和随机9 Mixed strategies in theory and tennis 混合战略的理论和网球10 Mixed strategies in baseball, dating and paying your taxes 混合战略棒球，约会和支付您的税11 Evolutionary stability: cooperation, mutation, and equilibrium 进化稳定：合作，突变，与平衡12 Evolutionary stability: social convention, aggression, and cycles 进化稳定：社会公约，侵略，和周期13 Sequential games: moral hazard, incentives, and hungry lions 顺序游戏：道德风险，奖励和饥饿的狮子14 Backward induction: commitment, spies, and first-mover advantages 落后的感应：承诺，间谍，和先行者优势15 Backward induction: chess, strategies, and credible threats 落后的感应：国际象棋，战略和可信的威胁16 Backward induction: reputation and duels 落后的感应：声誉和决斗17 Backward induction: ultimatums and bargaining 落后的感应：最后通牒和讨价还价18 Imperfect information: information sets and sub-game perfection 不完全信息：信息集和子博弈完美19 Subgame perfect equilibrium: matchmaking and strategic investments 子博弈完美均衡：招商引资和战略投资20 Subgame perfect equilibrium: wars of attrition 子博弈完美均衡：战争的消耗21 Repeated games: cooperation vs. the end game 重复博弈：合作与结局22 Repeated games: cheating, punishment, and outsourcing 重复博弈：作弊，惩罚和外包23 Asymmetric information: silence, signaling and suffering education 信息不对称：沉默，信令和苦难教育24 Asymmetric information: auctions and the winner's curse 信息不对称：拍卖和获奖者的诅咒学校介绍：耶鲁大学（Yale University）,旧译“耶劳大书院”，是一所坐落于美国康乃狄格州纽黑文市的私立大学，始创于1701年，初名“大学学院”（Collegiate School）。

耶鲁大学博弈论课堂笔记（一）第一节：导论——五个入门结论无论别人怎么选，如果选a的结果严格优于b，那么a相对于b是个严格优势策略。

结论一：不要选择严格劣势策略。

理由：如果我选择了优势策略，我在每次博弈都得到更好的收益。

结论二：理性的选择，使总结果变得糟糕。

（理性人的理性选择造成了次优的结果。

）——囚徒困境结论三：汝欲得之，必先知之。

结论四：站在别人的立场上去分析他们会怎么做。

结论五：耶鲁大学的学生都很自私。

第二节：学会换位思考博弈的要素有哪些？例：III博弈分析：不管i怎么选，中间总是优于右边，得出结论，参与者ii不应该选右。

（参与者i的策略s’i,严格劣于参与者i的另一个策略si,在其他参与者选择s-i时，此情况下选s’i的收益UI(s’i),对所有的s-i均成立。

）表达：s’i严格劣于si， Ui(si,s-i)>Ui(s’i,s-i) for all “s-i”.文字表述：如果si总是更好的选择，即总能给参与人i带来更高的收益，而无论其他参与人怎么选。

例：防线布置问题入侵者打算入侵一个国家，有两条路，必须通过其一才能进入，你是这个国家的防御者，要决定在哪个路口布置防线，只能防守二者之一。

一条路崎岖（途中会损失一个营的兵力），另一条路平坦，如果入侵者遇到了你布置的防线，不管哪条路都要再损失一个营的兵力入侵者收益为攻入国家时还剩多少兵力，防守者的收益为入侵者损失多少兵力。

分析：如果入侵者走eazy pass，你应防守 eazy pass（优于hard pass）；如果入侵者走hard pass，你应防守hard pass（优于eazy pass）结论：入侵者不会采取“弱劣势策略”崎岖之路是弱劣势策略，应在平坦之路设防。

（弱劣势策略）（参与者的策略s’i弱劣于其他策略si当且仅当在对手选s-i的情况下，参与人i选择si的收益等于对手选s-i下她选s’i的收益。

而且在任何情况下此条件均成立）表达：s’i弱劣于其他策略si ，Ui(si,s-i) >=Ui(s’i,s-i)耶鲁大学博弈论课堂笔记（二）第三节：迭代剔除和中位选民定理『迭代剔除』：例：政治模型案例假设有两个候选人，他们为了选举必须确定自己的政治立场，他们要从一系列政治主张中选择一个政治立场。

耶鲁博弈论24讲全笔记第一部分：博弈论的基础知识1、博弈论的定义及其在现实生活中的应用《耶鲁博弈论24讲全笔记》“1、博弈论的定义及其在现实生活中的应用”博弈论，这个引人入胜的学科，是一门研究决策问题的独特学科。

它的基本思想在于，把复杂多变的真实世界简化为具有明确规则和目标的多人决策问题。

在这个世界里，每一个参与者都需要根据其他参与者的策略来调整自己的决策，以期达到各自的目标。

博弈论起源于棋类游戏，如国际象棋和围棋，这些游戏的规则明确，且每个玩家都有可能成为赢家或输家。

然而，博弈论的应用远不止于此。

在现实世界中，博弈论的原理被广泛应用于政治、经济、生物、国际关系等多个领域。

在政治领域，博弈论可以帮助我们理解权力平衡和国际关系。

例如，囚徒困境就是一个经典的博弈论模型，它描述了两个囚犯因共同犯罪而受审的情况。

在这个情境中，两个囚犯都需要做出决策，是否选择揭发对方。

这个模型不仅可以解释为什么有时候合作会带来更大的利益，也可以揭示为什么有时候，即使个人利益最大化的选择也会导致集体的非最优结果。

在经济领域，博弈论更是具有广泛的应用。

例如，拍卖中的博弈论可以帮助我们理解为什么拍卖可以带来高昂的成交价，以及为什么有时候最低价拍卖可以带来最大的社会利益。

此外，博弈论还可以帮助我们理解市场垄断、价格竞争等复杂的市场行为。

在生物学领域，博弈论被用来解释生物种群的进化策略，如猎物的捕食者与被捕食者之间的动态关系。

在医学领域，博弈论也被用来理解和预测疾病的发展和传播。

总的来说，博弈论是一种独特的思考方式，它可以帮助我们理解真实世界中的决策和策略行为。

它的应用广泛，无论是在政治、经济、生物还是其他领域，都可以找到博弈论的应用实例。

通过学习博弈论，我们可以更好地理解真实世界中的决策过程，并找到更优的决策策略。

2、博弈的参与者、策略和结果《耶鲁博弈论24讲全笔记》是一本介绍博弈论的经典教材，第二讲“博弈的参与者、策略和结果”是其中的重要部分。

Syllabusby (course_default) — last modified 10—14-2008 04：00 PMDocument Actions•This course is an introduction to game theory and strategic thinking. Ideas such as dominance， backward induction， Nash equilibrium, evolutionary stability，commitment， credibility, asymmetric information， adverse selection, and signaling are discussed and applied to games played in class and to examples drawn from economics，politics, the movies, and elsewhere.ECON 159: Game Theory （Fall， 2007）SyllabusProfessor:Ben Polak, Professor of Economics and Management， Yale UniversityDescription：This course is an introduction to game theory and strategic thinking. Ideas such as dominance， backward induction， Nash equilibrium, evolutionary stability, commitment，credibility， asymmetric information, adverse selection， and signaling are discussed and applied to games played in class and to examples drawn from economics, politics, the movies， and elsewhere.Texts：A。

博弈论的读书笔记博弈论，乍一听这个词，可能会让人觉得高深莫测，仿佛是只有在经济学或数学的殿堂里才会被探讨的课题。

但实际上，它与我们的日常生活息息相关，从下棋打牌到商业谈判，从政治决策到人际关系，无处不在。

在我深入研读博弈论的过程中，有几个关键的概念给我留下了深刻的印象。

首先是“零和博弈”。

简单来说，就是一方的收益必然意味着另一方的损失，双方的利益总和为零。

比如在一场体育比赛中，只有一个冠军，一方的胜利就意味着其他方的失败。

这种博弈通常竞争激烈，参与者往往会全力以赴，争取自己的胜利。

但在现实生活中，零和博弈并不是最常见的情况，更多的是“非零和博弈”。

非零和博弈又分为“正和博弈”和“负和博弈”。

正和博弈是指参与各方的利益总和是增加的，大家可以通过合作实现共赢。

比如企业之间的合作研发，共同开拓市场，就能创造出比各自单独行动更大的价值。

而负和博弈则是各方的利益总和减少，典型的例子就是战争，不仅造成人员伤亡和财产损失，还会对社会经济发展产生巨大的负面影响。

博弈论中的“策略”也是一个核心要素。

每个参与者都需要根据对手的可能行动来选择自己的最优策略。

这让我想起了小时候玩的“石头剪刀布”游戏，看似简单，其实也蕴含着策略。

如果对手一直出石头，那么你下次出剪刀的概率就应该降低。

在更复杂的博弈中，策略的选择就更加重要。

比如在商业竞争中，企业需要考虑竞争对手的产品定位、价格策略、市场推广等，来制定自己的发展战略。

“纳什均衡”是博弈论中一个极其重要的概念。

它指的是一种状态，在这种状态下，每个参与者的策略都是对其他参与者策略的最优反应，没有人有动力去单方面改变自己的策略。

举个例子，假设有两家企业在竞争同一个市场，如果企业 A 采取降价策略，企业 B 也会跟着降价以保持竞争力；如果企业 A 提价，企业 B 可能会趁机扩大市场份额。

在这种情况下，可能会达到一个价格平衡点，双方都不愿意轻易改变策略，这就是纳什均衡。

博弈论还让我对“信息”的重要性有了新的认识。