[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》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；。

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。

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。

课时：2课时教学目标：1. 让学生了解博弈论的基本概念、原理和应用。

2. 培养学生的逻辑思维能力和决策能力。

3. 增强学生对现实生活中的博弈现象的认识。

教学重点：1. 博弈论的基本概念和原理。

2. 博弈论在现实生活中的应用。

教学难点：1. 博弈论模型的构建。

2. 博弈论在实际问题中的应用。

教学过程：第一课时一、导入1. 向学生介绍博弈论的定义和起源。

2. 通过生活中的实例，引导学生关注博弈现象。

二、基本概念1. 介绍博弈论的基本术语，如参与者、策略、收益等。

2. 讲解零和博弈、正和博弈、完全信息博弈和不完全信息博弈等概念。

三、博弈论原理1. 分析纳什均衡、混合策略均衡等核心原理。

2. 通过实例讲解博弈论原理在现实生活中的应用。

四、课堂练习1. 让学生分组讨论，分析一个现实生活中的博弈现象，并尝试运用博弈论原理进行分析。

2. 每组选派代表进行汇报，教师点评。

第二课时一、回顾与总结1. 回顾博弈论的基本概念、原理和应用。

2. 总结学生在课堂练习中的表现。

二、博弈论模型构建1. 介绍博弈论模型的基本要素，如参与者的数量、策略空间、收益矩阵等。

2. 通过实例讲解博弈论模型的构建过程。

三、博弈论在实际问题中的应用1. 分析博弈论在经济学、政治学、心理学等领域的应用。

2. 结合实际案例，讲解博弈论在实际问题中的应用。

四、课堂讨论1. 让学生分组讨论，分析一个与自己专业相关的博弈现象，并尝试运用博弈论原理进行分析。

2. 每组选派代表进行汇报，教师点评。

五、课后作业1. 让学生收集生活中的博弈现象，运用博弈论原理进行分析。

2. 下节课进行汇报。

教学反思：1. 本节课通过理论讲解和实例分析，让学生对博弈论有了初步的认识。

2. 课堂练习和讨论环节，激发了学生的学习兴趣，提高了学生的参与度。

3. 教师在讲解过程中，应注重引导学生思考，培养学生的逻辑思维能力和决策能力。

4. 在今后的教学中，可以结合更多实际案例，让学生更好地理解博弈论的应用。

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）。

耶鲁大学开放课程28科目：《耶鲁大学开放课程：有关食物的心理学，生物学和政治学》《耶鲁大学开放课程：美国内战与重建，1845-1877》《耶鲁大学开放课程：天体物理学之探索和争议》《耶鲁大学开放课程：进化，生态和行为原理》《耶鲁大学开放课程：1945年后的美国小说》《耶鲁大学开放课程：生物医学工程探索》《耶鲁大学开放课程：新约及其历史背景》《耶鲁大学开放课程：全球人口增长问题》《耶鲁大学开放课程：古希腊历史简介》《耶鲁大学开放课程：新生有机化学》《耶鲁大学开放课程：文学理论导论》《耶鲁大学开放课程：旧约全书导论》《耶鲁大学开放课程: 政治哲学导论》《耶鲁大学开放课程：心理学导论》《耶鲁大学开放课程—哲学：死亡》《耶鲁大学开放课程: 现代诗歌》《耶鲁大学开放课程：金融市场》《耶鲁大学开放课程：罗马建筑》《耶鲁大学开放课程: 解读但丁》《耶鲁大学开放课程：聆听音乐》《耶鲁大学开放课程：基础物理》《耶鲁大学开放课程：博弈论》《耶鲁大学开放课程: 弥尔顿》《我为什么选择耶鲁》哈佛大学开放课程：《幸福》《公正》普林斯顿大学开放课程：《领导能力简介》《国际座谈会》《自由意志定理》《技术世界的领导能力》《人性》牛津大学开放课程：《尼采的心灵与自然》《哲学概论》《哲学入门》《批判性推理入门》剑桥大学开放课程：《人类学》沃顿商学院开放课程：《沃顿知识在线》斯坦福大学开放课程：《iPhone开发教程》《编程模式(C和C++)》《抽象编程》《人机交互研讨》《编程方法学》《经济学》《人类健康之动态》《医学、健康及科学前沿》《力学》《狭义相对论》《广义相对论》《统计力学》《宇宙学》《量子纠缠1》《量子纠缠2》《线性动力系统教程》《JOBS演讲》麻省理工大学开放课程：《MIT计算机科学及编程导论》《算法导论》《生物学导论》《固体化学导论》《电磁学》《经典力学》《脑与认知科学》《电机工程与计算机科学》《数字通信原理》TTC开放课程：《经济学第3版》(TTC ）《全球化与爱情》《激情：感情的哲学与智慧教程》《21世纪的乌托邦及其恐怖行为》《莎士比亚》。

耶鲁大学网络公开课《博弈论》的字幕翻译
房纯倩;高军
【期刊名称】《江苏外语教学研究》
【年(卷),期】2017(000)001
【摘要】国外网络公开课在国内日益普及,但其字幕翻译仍存在一定问题和发展空间。

本文以耶鲁大学网络公开课《博弈论》的字幕翻译为例,从术语、语义和文化含义三个方面探讨网络公开课的翻译难点及解决方案。

【总页数】3页(P80-82)
【作者】房纯倩;高军
【作者单位】上海理工大学外国语学院
【正文语种】中文
【中图分类】G649.712
【相关文献】
1.网络公开课字幕翻译信息处理策略研究 [J], 梁晶晶;殷燕;贺井瑶;朱丹;张蓝艳;杨慕恩
2.从顺句驱动原则看网络公开课字幕翻译——以《了解欧洲》为例 [J], 魏燕萍;潘春雷
3.从顺句驱动原则看网络公开课字幕翻译——以《了解欧洲》为例 [J], 魏燕萍;潘春雷;
4.斯坦福大学网络公开课《如何创业》字幕翻译中Trados的应用 [J], 赵文龙; 庄天赐; 刘铭扬
5.网络公开课字幕翻译信息处理策略研究 [J], 梁晶晶;殷燕;贺井瑶;朱丹;张蓝艳;杨慕恩
因版权原因，仅展示原文概要，查看原文内容请购买。

博弈论作业（博弈论24讲）数应专业一、1、理性人：指代这一类人，他们只关心自己的利益。

2、如果选择a的结果严格优于b，那么就说a相对于b来说是一个严格优势策略。

结论：不要选择严格略施策略。

3、理性人的理性选择造成了次优的结果4、举例：囚徒困境、宿舍卫生打扫问题、企业打价格战等5、协和谬误收益很重要，“如欲得之，必先知之”6、要学会换位思考，站在别人的立场上看别人会怎么做，在考虑自己受益的同时，要注意别人会怎么选择二、1、打渔问题、全球气候变暖与碳排放问题2、博弈的要素：参与人、策略集合、收益3、如果策略a严格劣于策略b，那么不管他人怎么选择，b总是更好的选择4、军队的入侵与防卫问题5、所有人都从1到100中选个数字，最接近所有人选的数字的均值的2/3者为胜，这个数字是多少呢？作为理性人，每个人都会选择67（100*2/3）以下的数，进一步假设你的对手也是理性的，你会选择45（100*4/9）以下的数……依据哲学观点，如果大家都是理性程度相当的，那么最后数字将为1，然而结果却是9，这说明博弈的复杂性6、共同知识与相互知识的区别三、1、利用迭代剔除法领悟中间选民问题2、迭代剔除法就是严格下策反复消去法，不断地把劣势策略剔除出去，最后只剩下相对优势的策略3、中间选民问题就是，在两党制中，政党表述施政纲领要吸引位于中间位置的选民，他们认为在选举中处于中间标度可以吸引左右两边的选民，并以此获得胜利。

4、中间选民问题理论成立的条件是有两个参与人；政治立场能使选民相信。

5、由此延伸出来的还有加油站选址问题，两家加油站不是在不同的路口选址，而是在不确定哪个位置较佳的时候会选在同一处，这也是“中间选民定理”的凸显6、在迭代剔除法不能运用时，比如说该博弈中博弈方1和2均没有严格下策，可以用二维坐标系画出选择策略之后的收益分布四、1、罚点球：一个经过模型简化的点球模型：罚球者可以选择左路，中路，右路3种路线去踢点球，门将可以选择向左扑救或者向右扑救（门将没有傻站着不动的option）。

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。

耶鲁大学公开课：博弈论习题集1（第1-3讲内容）Ben Polak, Econ 159a/MGT522a.由人人影视博弈论制作组Darrencui翻译1.严格劣势策略与弱劣势策略：严格劣势策略的定义是什么？弱劣势策略的定义是什么？请用一个包含两个参与人的博弈矩阵来举例说明，要求其中一个参与人有三个策略且三者之一为严格劣势策略；另一个参与人有三个策略但三者之一为弱劣势策略。

请指出你所举例子中的劣势策略。

2.迭代剔除（弱）劣势策略：请看下面的博弈2(a). 这个博弈中是否存在严格劣势策略和弱劣势策略？如果存在，请指出并说明。

(b). 剔除掉严格劣势策略和弱劣势策略之后，在简化的博弈中是否还有劣势策略呢？如果是，请指出并说明。

最后哪些策略不会被剔除呢？(c). 回顾你第一次剔除劣势策略时哪些策略是劣势策略并给出解释。

把它与第二次剔除的劣势策略作比较。

从中你能得出关于迭代剔除劣势策略的何种结论？3. 霍特林的选址博弈（也称霍特林模型）：回顾一下课堂中所讲的选票博弈。

其中有两个参与人，每个参与人都从集合* +中选出自己的立场。

这十个立场均分全部的选票。

选民把选票投给与自己立场最接近的候选人。

如果两个候选人站在同一个立场上，那么持该立场选民的选票平均分给每个候选人。

候选人想要最大化自己的得票率。

举例来说，()。

而() [提示：回答这道题时不必画出整个矩阵](a).课堂中我们指出立场2严格优于立场1，而实际上还有其它的立场也是严格优于立场1的，请找出所有优于立场1的立场并作出解释。

(b).假设现在有三名候选人。

举例来说，()而()。

此时立场2是否严格优于立场1？立场3呢？请作出解释。

另外，假设我们剔除了立场1和10，但是该立场的选票依然存在。

在简化的博弈中，立场2是否严格劣于或弱劣于其它（纯）策略？请作出解释。

4. “到底谁的话语权更重”：由三人组成的评审委员会要决出一场全国艺术大赛的冠军。

经过激烈的讨论之后，有三名选手进入最后的获奖候选人名单，分别是：一名画城市中的羚羊的女画家、一名做铅盒的男工匠、一名做根雕的男雕塑家。

So this is Game Theory Economics 159.欢送来到经济学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--里面有一张授权书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.有一张初步教学大纲网站上也有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--他们用那张纸扇风呢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.比方说自由竞争企业Firms in perfect competition are price takers:这些企业是价格接受者they don't particularly have to worry about他们不必担忧the actions of their competitors.他们的竞争对手的策略You also saw firms that were monopolists又比方说垄断企业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.他们不是价格接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.比方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方美国人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.他们就可以到耶鲁网站观看这些视频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. 此时摄像时机转到你所在的方向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,你们的面前应该有张授权书you have to be able to sign it, and what that says is that授权书的大概内容是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,要是这令你很紧张if it's any consolation, it's making me very nervous.它会让我更紧张这权当抚慰了吧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内交上来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?那两张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内容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这也确实是本好书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,你们要是在网站上看了教学评估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.有人想帮助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.我们回忆一下刚刚进行的游戏"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内容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由此我就把这张纸上的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内容插入到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.我来做个示范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,单元格内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这样就把前两张表格的信息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内容的矩阵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.别紧张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,比方B-/B+这个范围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.你说的意思是压缩范围I'm not sure it does compress the range.但是我不太确定这是否压缩了范围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 分数范围会在B+到CI mean those are similar kind of ranges这两个范围大小差不多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.。