[耶鲁大学开放课程：博弈论].Problem.Set.2
耶鲁大学《博弈论》第二节课的代表符号、实例
耶鲁大学《博弈论》第二节课的代表符号、实例
耶鲁大学《博弈论》二
———代表符号、实例
博弈的组成要素：
参与人、策略、收益
博弈组成要素的代表符号：
参与人：小写i 和小写j(在上节课的数字游戏中，每个人都是参与人）
策略：si 为参与人i 的某个策略（如果i 在数字游戏中选择了数字13，那么13就等于si)
策略集合：大写Si ，即为参与人所有可能选择的策略集合（在数字游戏中为1、2、3到100）
策略组合：参与人所有策略的结合
除参与者，其它人的参与策略：s-i （可能是s1、s2、s3等等）收益：U （Ui 取决于参与人1的策略）
参与人Ui 取决于所有人的策略决定，简写为Ui(s)
数字游戏中参与人的结果：
1、赢、5美元减去误差；
2、输、一无所获。
（假设没有平局）
例图一：
Ⅱ
L C R
Ⅰ 上（T ）
下（B ）
问题1：Ⅰ有没有劣势策略？
问题2：Ⅱ有没有劣势策略？
定义：参参与者i 的策略严格劣于另一个参与者的策略，在其它人选择S-i ，选择si 的5、-1 11、3 0、0 6、4 0、2 2、0
收益Ui(si)严格优于此情况下选择s’i的收益Ui(s’i);
最重要的是这样的选择必须对所有S-i均成立。
例二
一个侵略者想侵入一个国家，有两条路可以通过，或者可以说成两个管卡，侵略者必须选择通过两个关卡中的一个，这两各关卡，一个关卡道路崎岖，侵略者经过的话会损失一个营，一个关卡平坦宽阔，侵略者经过这个关卡不会损失一兵一卒；
假设你是被侵略国家的将军，你会选择那个关卡防守？假设双方都知道你手上的兵力只能使侵略者损失一个营的兵力；。
耶鲁大学公开课英文讲义—博弈论第一节
Game Theory: Lecture 1 TranscriptProfessor 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 look at--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. 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. You saw firms working in perfect competition. Firms in perfect competition are price takers: they don't particularly have to worry about the actions of their competitors. You also saw firms that were monopolists and monopolists don't have any competitors to worry about, so that's not a particularly strategic situation. They're not price takers but they take the demand curve. Is this looking familiar for some of you who can remember doing 115 last year or maybe two years ago for some of you? Everything in between is strategic. So everything that constitutes imperfect competition is a strategic setting. Think about the motor industry, the motor car industry. Ford has to worry about what GM is doing and what Toyota is doing, and for the moment at least what Chrysler is doing but perhaps not for long. So there's a small number of firms and their actions affect each other.So for a literal definition of what strategic means: it's a setting where the outcomes that affect you depend on actions, not just on your own actions, but on actions of others. All right, that's as much as I'm going to say for preview right now, we're going to come back and see plenty of this over the course of the next semester.So what I want to do is get on to where this applies. It obviously applies in Economics, but it also applies in politics, and in fact, this class will count as a Political Science class if you're a Political Science major. You should go check with the DUS in Political Science. It count - Game Theory is very important in law these days. So for those of you--for the half of you--that aregoing to end up in law school, this is pretty good training. Game Theory is also used in biology and towards the middle of the semester we're actually going to see some examples of Game Theory as applied to evolution. And not surprisingly, Game Theory applies to sport.So let's talk about a bit of admin. How are you doing on filling out those games? Everyone managing to multitask: filling in Game 1? Keep writing. I want to get some admin out of the way and I want to start by getting out of the way what is obviously the elephant in the room. Some of you will have noticed that there's a camera crew here, okay. So as some of you probably know, Yale is undergoing an open education project and they're videoing several classes, and the idea of this, is to make educational materials available beyond the walls of Yale. In fact, on the web, internationally, so people in places, maybe places in the U.S. or places miles away, maybe in Timbuktu or whatever, who find it difficult to get educational materials from the local university or whatever, can watch certain lectures from Yale on the web.Some of you would have been in classes that do that before. What's going to different about this class is that you're going to be participating in it. The way we teach this class is we're going to play games, we're going to have discussions, we're going to talk among the class, and you're going to be learning from each other, and I want you to help people watching at home to be able to learn too. And that means you're going to be on film, at the very least on mike.So how's that going to work? Around the room are three T.A.s holding mikes. Let me show you where they are: one here, one here, and one here. When I ask for classroom discussions, I'm going to have one of the T.A.s go to you with a microphone much like in "Donahue" or something, okay. At certain times, you're going to be seen on film, so the camera is actually going to come around and point in your direction.Now I really want this to happen. I had to argue for this to happen, cause I really feel that this class isn't about me. I'm part of the class obviously, but it's about you teaching each other and participating. But there's a catch, the catch is, that that means you have to sign that legal release form.So you'll see that you have in front of you a legal release form, you have to be able to sign it, and what that says is that we can use you being shown in class. Think of this as a bad hair day release form. All right, you can't sue Yale later if you had a bad hair day. For those of you who are on the run from the FBI, your Visa has run out, or you're sitting next to your ex-girlfriend, now would be a good time to put a paper bag over your head.All right, now just to get you used to the idea, in every class we're going to have I think the same two people, so Jude is the cameraman; why don't you all wave to Jude: this is Jude okay. And Wes is our audio guy: this is Wes. And I will try and remember not to include Jude and Wes in the classroom discussions, but you should be aware that they're there. Now, if this is making you nervous, if it's any consolation, it's making me very nervous. So, all right, we'll try and make this class work as smoothly as we can, allowing for this extra thing. Let me just say, no one's making any money off this--at least I'm hoping these guys are being paid--but me and the T.A.s are not being paid. The aim of this, that I think is a good aim, it's an educational project, and I'm hoping you'll help us with it. The one difference it is going to mean, is that at times I might hold some of the discussions for the class, coming down into this part of the room, here, to make it a little easier for Jude.All right, how are we doing now on filling out those forms? Has everyone filled in their strategy for the first game? Not yet. Okay, let's go on doing a bit more admin. The thing you mostly care about I'm guessing, is the grades. All right, so how is the grade going to work for this class? 30% of the class will be on problem sets, 30% of the grade; 30% on the mid-term, and 40% on the final; so 30/30/40.The mid-term will be held in class on October 17th; that is also in your syllabus. Please don't anybody tell me late - any time after today you didn't know when the mid-term was and therefore it clashes with 17 different things. The mid-term is on October 17th, which is a Wednesday, in class. All right, the problem sets: there will be roughly ten problem sets and I'll talk about them more later on when I hand them out. The first one will go out on Monday but it will be due ten days later. Roughly speaking they'll be every week.The grade distribution: all right, so this is the rough grade distribution. Roughly speaking, a sixth of the class are going to end up with A's, a sixth are going to end up with A-, a sixth are going to end up with B+, a sixth are going to end up with B, a sixth are going to end up with B-, and the remaining sixth, if I added that up right, are going to end up with what I guess we're now calling the presidential grade, is that right?That's not literally true. I'm going to squeeze it a bit, I'm going to curve it a bit, so actually slightly fewer than a sixth will get straight A's, and fewer than a sixth will get C's and below. We'll squeeze the middle to make them be more B's. One thing I can guarantee from past experience in this class, is that the median grade will be a B+. The median will fall somewhere in the B+'s. Just as forewarning for people who have forgotten what a median is,that means half of you--not approximately half, it means exactly half of you--will be getting something like B+ and below and half will get something like B+ and above.Now, how are you doing in filling in the forms? Everyone filled them in yet? Surely must be pretty close to getting everyone filled in. All right, so last things to talk about before I actually collect them in - textbooks. There are textbooks for this class. The main textbook is this one, Dutta'sbook Strategy and Games. If you want a slightly tougher book, more rigorous book, try Joel Watson's book, Strategies. Both of those books are available at the bookstore.But I want to warn everybody ahead of time, I will not be following the textbook. I regard these books as safety nets. If you don't understand something that happened in class, you want to reinforce an idea that came up in class, then you should read the relevant chapters in the book and the syllabus will tell you which chapters to read for each class, or for each week of class, all right. But I will not be following these books religiously at all. In fact, they're just there as back up.In addition, I strongly recommend people read, Thinking Strategically. This is good bedtime reading. Do any of you suffer from insomnia? It's very good bedtime reading if you suffer from insomnia. It's a good book and what's more there's going to be a new edition of this book this year and Norton have allowed us to get advance copies of it. So if you don't buy this book this week, I may be able to make the advance copy of the new edition available for some of you next week. I'm not taking a cut on that either, all right, there's no money changing hands.All right, sections are on the syllabus sign up - sorry on the website, sign up as usual. Put yourself down on the wait list if you don't get into the section you want. You probably will get into the section you want once we're done. All right, now we must be done with the forms. Are we done with the forms? All right, so why don't we send the T.A.s, with or without mikes, up and down the aisles and collect in your Game #1; not Game #2, just Game #1.Just while we're doing that, I think the reputation of this class--I think--if you look at the course evaluations online or whatever, is that this class is reasonably hard but reasonably fun. So I'm hoping that's what the reputation of the class is. If you think this class is going to be easy, I think it isn't actually an easy class. It's actually quite a hard class, but I think I can guarantee it's going to be a fun class. Now one reason it's a fun class, is the nice thing about teaching Game Theory - quieten down folks--one thing about teaching Game Theory is, you get to play games, and that's exactlywhat we've just been doing now. This is our first game and we're going to play games throughout the course, sometimes several times a week, sometimes just once a week.We got all these things in? Everyone handed them in? So I need to get those counted. Has anyone taken the Yale Accounting class? No one wants to - has aspirations to be - one person has. I'll have a T.A. do it, it's all right,we'll have a T.A. do it. So Kaj, can you count those for me? Is that right? Let me read out the game you've just played."Game 1, a simple grade scheme for the class. Read the following carefully. Without showing your neighbor what you are doing, put it in the box below either the letter Alpha or the letter Beta. Think of this as a grade bid. I will randomly pair your form with another form and neither you nor your pair will ever know with whom you were paired. Here's how the grades may be assigned for the class. [Well they won't be, but we can pretend.] If you put Alpha and you're paired with Beta, then you will get an A and your pair a C. If you and your pair both put Alpha, you'll both get B-. If you put Beta and you're paired with Alpha, you'll get a C and your pair an A. If you and your pair both put Beta, then you'll both get B+."So that's the thing you just filled in.Now before we talk about this, let's just collect this information in a more useful way. So I'm going to remove this for now. We'll discuss this in a second, but why don't we actually record what the game is, that we're playing, first. So this is our grade game, and what I'm going to do, since it's kind of hard to absorb all the information just by reading a paragraph of text, I'm going to make a table to record the information. So what I'm going to do is I'm going to put me here, and my pair, the person I'm randomly paired with here, and Alpha and Beta, which are the choices I'm going to make here and on the columns Alpha and Beta, the choices my pair is making.In this table, I'm going to put my grades. So my grade if we both put Alpha is B-, if we both put Beta, was B+. If I put Alpha and she put a Beta, I got an A, and if I put Beta and she put an Alpha, I got a C. Is that correct? That's more or less right? Yeah, okay while we're here, why don't we do the same for my pair? So this is my grades on the left hand table, but now let's look at what my pair will do, what my pair will get.So I should warn the people sitting at the back that my handwriting is pretty bad, that's one reason for moving forward. The other thing I should apologize at this stage of the class is my accent. I will try and improve the handwriting, there's not much I can do about the accent at this stage.So once again if you both put Alpha then my pair gets a B-. If we both put Beta, then we both get a B+; in particular, my pair gets a B+. If I put Alpha and my pair puts Beta, then she gets a C. And if I put Beta and she puts Alpha, then she gets an A. So I now have all the information that was on the sheet of paper that you just handed in.Now there's another way of organizing this that's standard in Game Theory, so we may as well get used to it now on the first day. Rather then drawing two different tables like this, what I'm going to do is I'm going to take the second table and super-impose it on top of the first table. Okay, so let me do that and you'll see what I mean. What I'm going to do is draw a larger table, the same basic structure: I'm choosing Alpha and Beta on the rows, my pair is choosing Alpha and Beta on the columns, but now I'm going to put both grades in. So the easy ones are on the diagonal: you both get B- if we both choose Alpha; we both get B+ if we both choose Beta. But if I choose Alpha and my pair chooses Beta, I get an A and she gets a C. And if I choose Beta and she chooses Alpha, then it's me who gets the C and it's her who gets the A.So notice what I did here. The first grade corresponds to the row player, me in this case, and the second grade in each box corresponds to the column player, my pair in this case. So this is a nice succinct way of recording what was in the previous two tables. This is an outcome matrix; this tells us everything that was in the game.Okay, so now seems a good time to start talking about what people did. So let's just have a show of hands. How many of you chose Alpha? Leave your hands up so that Jude can catch that, so people can see at home, okay. All right and how many of you chose Beta? There's far more Alphas - wave your hands the Beta's okay. All right, there's a Beta here, okay. So it looks like a lot of - well we're going to find out, we're going to count--but a lot more Alpha's than Beta's. Let me try and find out some reasons why people chose.So let me have the Alpha's up again. So, the woman who's in red here, can we get a mike to the - yeah, is it okay if we ask you? You're not on the run from the FBI? We can ask you why? Okay, so you chose Alpha right? So why did you choose Alpha?Student: [inaudible] realized that my partner chose Alpha, therefore I chose [inaudible].Professor Ben Polak: All right, so you wrote out these squares, you realized what your partner was going to do, and responded to that. Any otherreasons for choosing Alpha around the room? Can we get the woman here? Try not to be intimidated by these microphones, they're just mikes. It's okay.Student: The reason I chose Alpha, regardless of what my partner chose, I think there would be better outcomes than choosing Beta.Professor Ben Polak: All right, so let me ask your names for a second-so your name was?Student: Courtney.Professor Ben Polak: Courtney and your name was?Student: Clara Elise.Professor Ben Polak: Clara Elise. So slightly different reasons, same choice Alpha. Clara Elise's reason - what did Clara Elise say? She said, no matter what the other person does, she reckons she'd get a better grade if she chose Alpha. So hold that thought a second, we'll come back to - is it Clara Elise, is that right? We'll come back to Clara Elise in a second. Let's talk to the Beta's a second; let me just emphasize at this stage there are no wrong answers. Later on in the class there'll be some questions that have wrong answers. Right now there's no wrong answers. There may be bad reasons but there's no wrong answers. So let's have the Beta's up again. Let's see the Beta's. Oh come on! There was a Beta right here. You were a Beta right? You backed off the Beta, okay. So how can I get a mike into a Beta? Let' s stick in this aisle a bit. Is that a Beta right there? Are you a Beta right there? Can I get the Beta in here? Who was the Beta in here? Can we get the mike in there? Is that possible? In here - you can leave your hand so that - there we go. Just point towards - that's fine, just speak into it, that's fine. Student: So the reason right?Professor Ben Polak: Yeah, go ahead.Student: I personally don't like swings that much and it's the B-/B+ range, so I'd much rather prefer that to a swing from A to C, and that's my reason. Professor Ben Polak: All right, so you're saying it compresses the range.I'm not sure it does compress the range. I mean if you chose Alpha, you're swinging from A to B-; and from Beta, swinging from B+ to C. I mean those are similar kind of ranges but it certainly is a reason. Other reasons for choosing? Yeah, the guy in blue here, yep, good. That's all right. Don't hold the mike; just let it point at you, that's fine.Student: Well I guess I thought we could be more collusive and kind of work together, but I guess not. So I chose Beta.Professor Ben Polak: There's a siren in the background so I missed the answer. Stand up a second, so we can just hear you.Student: Sure.Professor Ben Polak: Sorry, say again.Student: Sure. My name is Travis. I thought we could work together, but I guess not.Professor Ben Polak: All right good. That's a pretty good reason. Student: If you had chosen Beta we would have all gotten B+'s but I guess not.Professor Ben Polak: Good, so Travis is giving us a different reason, right? He's saying that maybe, some of you in the room might actually care about each other's grades, right? I mean you all know each other in class. You all go to the same college. For example, if we played this game up in the business school--are there any MBA students here today? One or two. If we play this game up in the business school, I think it's quite likely we're going to get a lot of Alpha's chosen, right? But if we played this game up in let's say the Divinity School, all right and I'm guessing that Travis' answer is reflecting what you guys are reasoning here. If you played in the Divinity School, you might think that people in the Divinity School might care about other people's grades, right? There might be ethical reasons--perfectly good, sensible, ethical reasons--for choosing Beta in this game. There might be other reasons as well, but that's perhaps the reason to focus on. And perhaps, the lesson I want to draw out of this is that right now this is not a game. Right now we have actions, strategies for people to take, and we know what the outcomes are, but we're missing something that will make this a game. What are we missing here?Student: Objectives.Professor Ben Polak: We're missing objectives. We're missing payoffs. We're missing what people care about, all right. So we can't really start analyzing a game until we know what people care about, and until we know what the payoffs are. Now let's just say something now, which I'll probably forget to say in any other moment of the class, but today it's relevant.Game Theory, me, professors at Yale, cannot tell you what your payoff should be. I can't tell you in a useful way what it is that your goals in life should be or whatever. That's not what Game Theory is about. However, once we know what your payoffs are, once we know what your goals are, perhaps Game Theory can you help you get there.So we've had two different kinds of payoffs mentioned here. We had the kind of payoff where we care about our own grade, and Travis has mentioned the kind of payoff where you might care about other people's grades. And what we're going to do today is analyze this game under both those possible payoffs. To start that off, let's put up some possible payoffs for the game. And I promise we'll come back and look at some other payoffs later. We'll revisit the Divinity School later.All right, so here once again is our same matrix with me and my pair, choosing actions Alpha and Beta, but this time I'm going to put numbers in here. And some of you will perhaps recognize these numbers, but that's not really relevant for now. All right, so what's the idea here? Well the first idea is that these numbers represent utiles or utilities. They represent what these people are trying to maximize, what they're to achieve, their goals.The idea is - just to compare this to the outcome matrix - for the person who's me here, (A,C) yields a payoff of--(A,C) is this box--so (A,C) yields a payoff of three, whereas (B-,B-) yields a payoff of 0, and so on. So what's the interpretation? It's the first interpretation: the natural interpretation that a lot of you jumped to straight away. These are people--people with these payoffs are people--who only care about their own grades. They prefer an A to a B+, they prefer a B+ to a B-, and they prefer a B- to a C. Right, I'm hoping I the grades in order, otherwise it's going to ruin my curve at the end of the year. So these people only care about their own grades. They only care about their own grades.What do we call people who only care about their own grades? What's a good technical term for them? In England, I think we refer to these guys - whether it's technical or not - as "evil gits." These are not perhaps the most moral people in the universe. So now we can ask a different question. Suppose, whether these are actually your payoffs or not, pretend they are for now. Suppose these are all payoffs. Now we can ask, not what did you do, but what should you do? Now we have payoffs that can really switch the question to a normative question: what should you do? Let's come back to - was it Clara Elise--where was Clara Elise before? Let's get the mike on you again. So just explain what you did and why again.Student: Why I chose Alpha?Professor Ben Polak: Yeah, stand up a second, if that's okay.Student: Okay.Professor Ben Polak: You chose Alpha; I'm assuming these were roughly your payoffs, more or less, you were caring about your grades.Student: Yeah, I was thinking -Professor Ben Polak: Why did you choose Alpha?Student: I'm sorry?Professor Ben Polak: Why did you choose Alpha? Just repeat what you said before.Student: Because I thought the payoffs - the two different payoffs that I could have gotten--were highest if I chose Alpha.Professor Ben Polak: Good; so what Clara Elise is saying--it's an important idea--is this (and tell me if I'm paraphrasing you incorrectly but I think this is more or less what you're saying): is no matter what the other person does, no matter what the pair does, she obtains a higher payoff by choosing Alpha. Let's just see that. If the pair chooses Alpha and she chooses Alpha, then she gets 0. If the pair chooses Alpha and she chose Beta, she gets -1. 0 is bigger than -1. If the pair chooses Beta, then if she chooses Alpha she gets 3, Beta she gets 1, and 3 is bigger than 1. So in both cases, no matter what the other person does, she receives a higher payoff from choosing Alpha, so she should choose Alpha. Does everyone follow that line of reasoning? That's a stronger line of reasoning then the reasoning we had earlier. So the woman, I have immediately forgotten the name of, in the red shirt, whose name was -Student: Courtney.Professor Ben Polak: Courtney, so Courtney also gave a reason for choosing Alpha, and it was a perfectly good reason for choosing Alpha, nothing wrong with it, but notice that this reason's a stronger reason. It kind of implies your reason.So let's get some definitions down here. I think I can fit it in here. Let's try and fit it in here.Definition: We say that my strategy Alpha strictly dominates my strategy Beta, if my payoff from Alpha is strictly greater than that from Beta, [and this is the key part of the definition], regardless of what others do.Shall we just read that back? "We say that my strategy Alpha strictly dominates my strategy Beta, if my payoff from Alpha is strictly greater than that from Beta, regardless of what others do." Now it's by no means my main aim in this class to teach you jargon. But a few bits of jargon are going to be helpful in allowing the conversation to move forward and this is certainly one. "Evil gits" is maybe one too, but this is certainly one.Let's draw out some lessons from this. Actually, so you can still read that, let me bring down and clean this board. So the first lesson of the class, and there are going to be lots of lessons, is a lesson that emerges immediately from the definition of a dominated strategy and it's this. So Lesson One of the course is:do not play a strictly dominated strategy. So with apologies to Strunk and White, this is in the passive form, that's dominated, passive voice. Do not play a strictly dominated strategy. Why? Somebody want to tell me why? Do you want to get this guy? Stand up - yeah.Student: Because everyone's going to pick the dominant outcome and then everyone's going to get the worst result - the collectively worst result.Professor Ben Polak: Yeah, that's a possible answer. I'm looking for something more direct here. So we look at the definition of a strictly dominated strategy. I'm saying never play one. What's a possible reason for that? Let's - can we get the woman there?Student: [inaudible]Professor Ben Polak: "You'll always lose." Well, I don't know: it's not about winning and losing. What else could we have? Could we get this guy in the pink down here?Student: Well, the payoffs are lower.Professor Ben Polak: The payoffs are lower, okay. So here's an abbreviated version of that, I mean it's perhaps a little bit longer. The reason I don't want to play a strictly dominated strategy is, if instead, I play the strategy that dominates it, I do better in every case. The reason I never want to play a strictly dominated strategy is, if instead I play the strategy that dominates it, whatever anyone else does I'm doing better than I would have done. Now that's a pretty convincing argument. That sounds like a convincing argument. It sounds like too obvious even to be worth stating in class, so let me now try and shake your faith a little bit in this answer.。
耶鲁大学开放课程博弈论笔记
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。
(完整版)耶鲁大学公开课博弈论原版资料
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。
(完整word)耶鲁大学博弈论_精简版
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。
耶鲁公开课--博弈论笔记
耶鲁公开课—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——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。
随着研制工作的深入，他们更是无法做出停止研制工作的决定。
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 耶鲁大学公开课 转
博弈论_耶鲁公开课__笔记及扩展1.博弈（game theory）构成要素：参与人players：i，j策略集strategy set:Si 策略si s-i 最优战略si*效益（目标）payoff：Ui Ui（s1，。
si。
sn）博弈game：G={S1，S2....Sn；U1，U2....Un}2.博弈论简史理论提出：1944 冯诺依曼（计算机之父、博弈论之父）与摩根斯坦恩合作出版《博弈论与经济行为》提出了博弈概念；提出了零和博弈（Zero-sum game）；引进了合作博弈理论发展：a.奠定非合作博弈基石：1950 Tucker 提出了“囚徒困境”；1950-1951 纳什：引入纳什均衡，将博弈论从零和博弈推进到非零和博弈；定义非合作博弈并证明纳什均衡存在；1994年诺贝尔经济学奖（与selten harsanyi共同拿到）b.1965-1975 泽尔腾Selten 将纳什均衡推广到动态博弈并提出子博弈精炼均衡；发展了倒退归纳分析方法；提出颤抖手均衡c.1967-1968 海萨尼harsanyi将纳什均衡推广到非完全信息博弈并突出贝叶斯均衡3.博弈的分类是否合作合作博弈cooperative ganme 非合作博弈non-operative ganme 一般说博弈指后者后者又分一下四类根据：是否完全信息是否同时进行完全信息静态博弈（囚徒困境prison's dilemma）纳什均衡Nash equilibrium完全信息动态信息（抢劫博弈）子博弈精炼均衡subgame perfect Nash equilibrium非完全信息静态博弈（密封报价拍卖模型）贝叶斯纳什均衡Bayesian Nash equilibrium非完全信息动态博弈（就业市场信号黔驴技穷）精炼贝叶斯纳什均衡perfect Bayesian Nash equilibrium完全信息complete information与完美信息perfect information完全信息指每个参与者都知道其他人的可行策略以及收益（支付函数），如果一个博弈不是完全信息，那么参与者就不可能知道自己的行为对其他博弈者的影响完美信息指参与者对其他参与者行动action的完全知识的状态，并随信息的出现而更新。
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耶鲁大学公开课：博弈论
习题集2（第4-5讲内容）
Ben Polak, Econ 159a/MGT522a.
由人人影视博弈论制作组Darrencui翻译
1.回顾罚球的案例：裁判判罚给参与人1一次点球的机会，参与人1即将执行判罚。
她有三种射门路径：左路、中路、右路。
参与人2是门将。
他可以选择防守左路、中路或者右路。
两名参与人的行为同时发出。
收益（以达成目概率的十倍计算）如下：
2
(a). 对于每一个参与人来说，有哪个策略严格劣于另一个（纯）策略吗？
(b). 在对参与人1的策略存在何种信念下，参与人2会觉得策略m是最佳对策？在对参与人2的策略存在何种信念下，参与人1会觉得策略M是最佳对策？[提示：本题不需要绘制三维图像！]
(c). 假设参与人2站在参与人1的立场上思考后发现，无论参与人1存在何种信念，她都会选择改信念下的最佳对策。
在这种情况下，参与人2是否应该选择策略m呢？
(d). 这个博弈是否存在（纯策略）纳什均衡？
2.回顾合伙人案例（Watson书中习题）：回顾一下我们在第四讲中提到的商业合伙人的案例。
两名律师合伙开了一家律师事务所并且平分收益。
每名律师都要各自打算一下自己要为事务所付出多少劳动。
事务所的收入按照如下公式计算：，其中、分别表示律师1和律师2付出的劳动量。
参数反映了两人的协同效果：一名律师付出越多的辛劳，合伙人就会获得越多的收益。
假设并且。
两名律师的收益分别是：
其中表示劳动的成本（注意：边际成本递增）。
假设这家律师事务所没有其它的开销。
在课堂上我们论证了，理性策略（即迭代剔除非最佳对策后剩余的策略）是
(a). 假设两名律师达成一致，决定两个人都付出一样多的劳动，并通过合同的形式规定了劳动量的指标。
如果他们想要最大化净收益（即收益减去劳动成本），他们应该在合同中规定各自付出多大的劳动量呢？这与课堂上得出的理性策略的劳动量相比有什么不同？[提示：为了解题方便，可以暂时考虑b=0的特殊情况]
(b). 假设第(a)题中的合同只对合伙人2有约束力，即合伙人2需要按照要求中的付出等量的劳动，而合伙人1可以任意在[0,4]的劳动量中自由选择。
合伙人1会选择付出多少劳动呢？这与
和有什么不同吗？请给出简明的解释。
(c). 回到最开始的博弈状态，假设现在，即合伙人的辛勤劳动起到了反协同效果。
求出这种情况下的最佳对策函数，并绘制相应的函数图像，找出这种情况下对应的理性策略。
把它与(a)中的指标作比较。
[提示：并不需要重做(a)的全部过程]
3. 纳什均衡与迭代剔除（Gibbons教科书上的习题）：请看下面的这个博弈：
(a). 哪些策略不会被迭代剔除严格劣势策略的过程剔除？
(b). 找出此博弈的（纯策略）纳什均衡
(c). 请尽可能详尽地解释说明，通常情况下（并不要局限于此博弈），组成纳什均衡的策略是否无法被迭代剔除严格劣势策略的过程剔除？
4. 分钱计划（Gibbons教科书中习题）：参与人1和参与人2因为如何分配10美元的问题争执不休。
每个参与人都说出了一个自己预期金额，该金额在0到10之间且允许出现小数。
两人需要同时做出选择。
参与人的收益就是她分得的钱款。
这个博弈有两条规则。
无论按哪条规则来分钱，如果出现的情况，每人获得自己的预期金额，剩余的钱款被销毁。
(a).第一条规则是，如果，那么每个参与人都一无所获并且钱会被销毁。
这种情况下的（纯策略）纳什均衡是什么？
(b).第二条规则是，如果，并且每个人的预期金额是不同的，那么预期金额最小的参与人分得等值的钱款而剩余的钱款归另一个参与人。
如果，并且，那么每个人都分得5美元。
这种情况下的（纯策略）纳什均衡是什么？
(c).假如我们为前两条规则增加一个限制条件，即预期金额必须是整数。
这是否会改变前两条规则下的（纯策略）纳什均衡？。