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  • 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 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 are going 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 17^(th);

  • 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 17^(th), 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's book 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 exactly what 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 other reasons 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. You're somebody who's wanted by

  • the FBI, right? Okay, so how about the

  • following argument? Look at the payoff matrix again

  • and suppose I reason as follows. Suppose I reason and say if we,

  • me and my pair, both reason this way and choose

  • Alpha then we'll both get 0. But if we both reasoned a

  • different way and chose Beta, then we'll both get 1.

  • So I should choose Beta: 1 is bigger than 0,

  • I should choose Beta. What's wrong with that argument?

  • My argument must be wrong because it goes against the

  • lesson of the class and the lessons of the class are gospel

  • right, they're not wrong ever,

  • so what's wrong with that argument?

  • Yes, Ale - yeah good. Student: Well because

  • you have to be able to agree, you have to be able to speak to

  • them but we aren't allowed to show our partners what we wrote.

  • Professor Ben Polak: All right, so it involves some

  • notion of agreeing. So certainly part of the

  • problem here, with the reasoning I just gave

  • you--the reasoning that said I should choose Beta,

  • because if we both reason the same way, we both do better that

  • way--involves some kind of magical reasoning.

  • It's as if I'm arguing that if I reason this way and reason

  • myself to choosing Beta, somehow I'm going to make the

  • rest of you reason the same way too.

  • It's like I've got ESP or I'm some character out of the X-Men,

  • is that what it's called? The X-Men right?

  • Now in fact, this may come as a surprise to

  • you, I don't have ESP, I'm not a character out of the

  • X-Men, and so you can't actually see

  • brain waves emitting from my head, and my reasoning doesn't

  • affect your reasoning. So if I did reason that way,

  • and chose Beta, I'm not going to affect your

  • choice one way or the other. That's the first thing that's

  • wrong with that reasoning. What else is wrong with that

  • reasoning? Yeah, that guy down here.

  • Student: Well, the second that you choose Beta

  • then someone's going - it's in someone's best interest to take

  • advantage of it. Professor Ben Polak: All

  • right, so someone's going to take advantage of me,

  • but even more than that, an even stronger argument:

  • that's true, but even a stronger argument.

  • Well how about this? Even if I was that guy in the

  • X-Men or the Matrix or whatever it was, who could reason his way

  • into making people do things. Even if I could make everyone

  • in the room choose Beta by the force of my brain waves,

  • what should I then do? I should choose Alpha.

  • If these are my payoffs I should go ahead and choose Alpha

  • because that way I end up getting 3.

  • So there's two things wrong with the argument.

  • One, there's this magical reasoning aspect,

  • my reasoning is controlling your actions.

  • That doesn't happen in the real world.

  • And two, even if that was the case I'd do better to myself

  • choose Alpha. So, nevertheless,

  • there's an element of truth in what I just said.

  • It's the fact that there's an element of truth in it that

  • makes it seem like a good argument.

  • The element of truth is this. It is true that by both

  • choosing Alpha we both ended up with B-'s.

  • We both end up with payoffs of 0, rather than payoffs of 1.

  • It is true that by both choosing, by both following this

  • lesson and not choosing the dominated strategy Beta,

  • we ended up with payoffs, (0,0), that were bad.

  • And that's probably the second lesson of the class.

  • So Lesson 2, and this lesson probably

  • wouldn't be worth stating, if it wasn't for sort of a

  • century of thought and economics that said the opposite.

  • So rational choice [in this case, people not choosing a

  • dominated strategy; people choosing a dominant

  • strategy] rational choice can lead to

  • outcomes that - what do Americans call this?--that

  • "suck." If you want a more technical

  • term for that (and you remember this from Economics 115),

  • it can lead to outcomes that are "inefficient,"

  • that are "Pareto inefficient," but "suck" will do for today.

  • Rational choices by rational players, can lead to bad

  • outcomes. So this is a famous example for

  • this reason. It's a good illustration of

  • this point. It's a famous example.

  • What's the name of this example, somebody?

  • This is called Prisoner's Dilemma.

  • How many of you have heard of the Prisoner's Dilemma before?

  • Most of you saw it in 115, why is it called the Prisoner's

  • Dilemma? Yes, the guy here in orange.

  • That's okay; he can just point at you that's

  • fine. Student: I think it's

  • whether or not the prisoner's cooperate in the sentence they

  • have, and if they kind of rat out the

  • other person, then they can have less;

  • but if both rat out, then they like end up losing

  • large scale. Professor Ben Polak:

  • Good, so in the standard story you've got these two crooks,

  • or two accused crooks, and they're in separate cells

  • and they're being interviewed separately--kept apart--and

  • they're both told that if neither of them rats the other

  • guy out, they'll go to jail for say a

  • year. If they both rat each other

  • out, they'll end up in jail for two years, But if you rat the

  • other guy out and he doesn't rat you out,

  • then you will go home free and he'll go to jail for five years.

  • Put that all down and you pretty quickly see that,

  • regardless whether the other guy rats you or not,

  • you're better off ratting him out.

  • Now, if you have never seen that Prisoner's Dilemma,

  • you can see it pretty much every night on a show called

  • Law & Order. How many of you have seen

  • Law & Order? If you haven't seen Law

  • & Order, the way to see Law &

  • Order is to go to a random TV set,

  • at a random time, and turn on a random channel.

  • This happens in every single episode, so much so that if any

  • of you actually - I mean this might actually be true at

  • Yale--but if you any of you or the TV guys: if any of you know

  • the guy who writes the plots for this,

  • have him come to the class (so I guess to see the video now)

  • and we get some better plot lines in there.

  • But, of course, that's not the only example.

  • The grade game and this is not the only example.

  • There are lots of examples of Prisoner's Dilemmas out there.

  • Let's try and find some other ones.

  • So how many of you have roommates in your college?

  • How many of you have roommates? Most of you have roommates

  • right? So I'm guessing now,

  • I won't make you show your hands, because it's probably

  • embarrassing, but what is the state of your

  • dorm rooms, your shared dorm rooms, at the end of the

  • semester or the end of the school year?

  • So I'm just guessing, having been in a few of these

  • things over the years, that by the end of the

  • semester, or certainly by the end of the

  • school year, the state of the average Yale dorm room is quite

  • disgusting. Why is it disgusting?

  • It's disgusting because people don't tidy up.

  • They don't clean up those bits of pizza and bits of chewed

  • bread and cheese, but why don't they tidy up?

  • Well let's just work it out. What would you like to happen

  • if you're sharing a dorm room? You'd like to have the other

  • guy tidy up, right? The best thing for you is to

  • have the other guy tidy up and the worst thing for you is to

  • tidy up for the other guy. But now work it out:

  • it's a Prisoner's Dilemma. If the other guy doesn't tidy

  • up, you're best off not tidying up either, because the last

  • thing you want is to be tidying up for the other guy.

  • And if the other guy does tidy up, hey the room's clean,

  • who cares? So either way,

  • you're not going to tidy up and you end up with a typical Yale

  • dorm room. Am I being unfair?

  • Are your dorm rooms all perfect? This may be a gender thing but

  • we're not going to go there. So there are lots of Prisoner's

  • Dilemmas out there, anyone got any other examples?

  • Other examples? I didn't quite hear that, sorry.

  • Let's try and get a mike on it so we can really hear it.

  • Student: [inaudible] Professor Ben Polak:

  • Okay, in divorce struggles, okay.

  • You're too young to be worrying about such things but never

  • mind. Yeah, okay, that's a good

  • example. All right, hiring lawyers,

  • bringing in big guns. What about an Economics example?

  • What about firms who are competing in prices?

  • Both firms have an incentive to undercut the other firm,

  • driving down profits for both. The last thing you want is to

  • have the other firm undercut you, in an attempt to push

  • prices down. That's good for us the

  • consumers, but bad for the firm, bad for industry profit.

  • What remedies do we see? We'll come back to this later

  • on in the class, but let's have a preview.

  • So what remedies do we see in society for Prisoner's Dilemmas?

  • What kind of remedies do we see? Let me try and get the guy here

  • right in front. Student: Collusion.

  • Professor Ben Polak: Collusion;

  • so firms could collude. So what prevents them from

  • colluding? One thing they could do,

  • presumably, is they could write a contract, these firms.

  • They could say I won't lower my prices if you don't lower your

  • prices, and they could put this contract in with the pricy

  • lawyer, who's taking a day off from the

  • divorce court, and that would secure that they

  • wouldn't lower prices on each other.

  • Is that right? So why wouldn't that work?

  • Why wouldn't writing a contract here work?

  • It's against the law. It's an illegal contract.

  • What about you with your roommates?

  • How many of you have a written contract, stuck with a magnet on

  • the fridge, telling you, when you're supposed to tidy

  • up. Very few of you.

  • Why do you manage to get some cooperation between you and your

  • roommates even without a written contract?

  • Student: It's not legally enforceable.

  • Professor Ben Polak: Well it probably is legally

  • enforceable actually. This guy says not,

  • but it probably is legally enforceable.

  • He probably could have a written contract about tidying

  • up. The woman in here.

  • Student: Repetition; you do it over and over.

  • Professor Ben Polak: Yeah, so maybe even among your

  • roommates, maybe you don't need a contract because you can

  • manage to achieve the same ends, by the fact that you're going

  • to be interacting with the same person, over and over again

  • during your time at Yale. So we'll come back and revisit

  • the idea that repeating an interaction may allow you to

  • obtain cooperation, but we're not going to come

  • back to that until after the mid-term.

  • That's way down the road but we'll get there.

  • Now one person earlier on had mentioned something about

  • communication. I think it was somebody in the

  • front, right? So let's just think about this

  • a second. Is communication the problem

  • here? Is the reason people behave

  • badly--I don't know "badly"--people choose Alpha in

  • this game here, is it the fact that they can't

  • communicate? Suppose you'd been able to talk

  • before hand, so suppose the woman here whose name

  • was…? Student: Mary.

  • Professor Ben Polak: …Mary,

  • had been able to talk to the person next to her whose name

  • is…? Student: Erica.

  • Professor Ben Polak: Erica.

  • And they said, suppose we know we're going to

  • be paired together, I'll choose Beta if you choose

  • Beta. Would that work?

  • Why wouldn't that work? Student: There's no

  • enforcement. Professor Ben Polak:

  • There's no enforcement. So it isn't a failure of

  • communication per se. A contract is more then

  • communication, a contract is communication

  • with teeth. It actually changes the payoffs.

  • So I could communicate with Alice on agreements,

  • but back home I'm going to go ahead and choose Alpha anyway;

  • all the better if he's choosing Beta.

  • So we'll come back and talk about more of these things as

  • the course goes on, but let's just come back to the

  • two we forgot there: so the collusion case and the

  • case back in Law & Order with the prisoners in the

  • cell. How do they enforce their

  • contracts? They don't always rat each

  • other out and some firms manage to collude?

  • How do they manage to enforce those contracts?

  • Those agreements, how are they enforced?

  • Student: They trust each other.

  • Professor Ben Polak: It could be they trust each other,

  • although if you trust a crook that's not

  • What else could it be? The guy here again with the

  • beard, yeah. Student: Could be a zero

  • sum game. Professor Ben Polak:

  • Well, but this is the game. So here's the game.

  • Student: No, but the pay,

  • the way they value, the way of valuing each--

  • Professor Ben Polak: Okay, so the payoffs may be

  • different. I have something simpler in

  • mind. Suppose they have a written

  • contract, or even an unwritten contract, what enforces the

  • contract for colluding firms or crooks in jail?

  • Yeah. Student: Gets off Scott

  • free in five years when the other guy gets out,

  • he might run into a situation where [inaudible]

  • Professor Ben Polak: Yeah,

  • so a short version of that is, it's a different kind of

  • contract. If you rat someone out in jail,

  • someone puts a contract out on you.

  • Tony Soprano enforces those contracts.

  • That's the purpose of Tony Soprano.

  • It's the purpose of the mafia. The reason the mafia thrives in

  • countries where it's hard to write legal contracts--let's say

  • some new parts of the former Soviet Union or some parts of

  • Africa--the reason the mafia thrives in those environments,

  • is that it substitutes for the law and enforces both legal and

  • illegal contracts. So I promised a while ago now,

  • that we were going to come back and look at this game under some

  • other possible payoffs. So I wasn't under a contract

  • but let's come back and fulfill that promise anyway.

  • So we're going to revisit, if not the Divinity School,

  • at least in people who have more morality than my friends up

  • in the business school. We're going to ask for the same

  • grade game we played at the beginning.

  • What would happen if player's payoffs looked different?

  • So these are "possible payoffs (2)."

  • I'll give these a name.. We called the other guys "evil

  • gits." We'll call these guys "indignant angels."

  • I can never spell indignant.. Is that roughly right?

  • Does that look right? I think it's right.

  • In-dig-nant isn't it: indignant. Indignant angels,

  • and we'll see why in a second. So here are their payoffs and

  • once again the basic structure of the game hasn't changed.

  • It's still I'm choosing Alpha and Beta, my pair is choosing

  • Alpha and Beta, and the grades are the same as

  • they were before. They're hidden by that board

  • but you saw them before. But this time the payoffs are

  • as follows. On the lead diagonal we still

  • have (0,0) and (1,1). But now the grades here are

  • -1--I'm sorry--the payoffs are -1 and -3, and here they're -3

  • and -1. What's the idea here?

  • These aren't the only other possible payoffs.

  • It's just an idea. Suppose I get an A and my pair

  • gets a C, then sure I get that initial payoff of 3,

  • but unfortunately I can't sleep at night because I'm feeling so

  • guilty. I have some kind of moral

  • conscience and after I've subtracted off my guilt feelings

  • I end up at -1, so think of this as guilt:

  • some notion of morality. Conversely, if I chose a Beta

  • and my pair chooses an Alpha, so I end up with a C and she

  • ends up with an A, then you know I have a bad time

  • explaining to my parents why I got a C in this class,

  • and I have to say about how I'm going to be president anyway.

  • But then, in addition, I feel indignation against this

  • person. It isn't just that I got a C;

  • I got a C because she made me get a C, so that moral

  • indignation takes us down to -3. So again, I'm not claiming

  • these are the only other possible payoffs,

  • but just another possibility to look at.

  • So suppose these were the payoffs in the game.

  • Again, suspend disbelief a second and imagine that these

  • actually are your payoffs, and let me ask you what you

  • would have done in this case. So think about it a second.

  • Write it down. Write down what you're going to

  • do on the corner of your notepad.

  • Just write down an Alpha or Beta: what you're going to do

  • here. You're not all writing.

  • The guy in the England shirt isn't writing.

  • You've got to be writing if you are in an England shirt.

  • Show it to your neighbor. Let's have a show of hands,

  • again I want you to keep your hands up so that Jude can see it

  • now. So how many of you chose Alpha

  • in this case? Raise your hands.

  • Come on, don't be shy. Raise your hands.

  • How many chose Beta in this case?

  • How many people abstained? Not allowed to abstain:

  • let's try it again. Alpha in this case?

  • No abstentions here. Beta in this case?

  • So we're roughly splitting the room.

  • Someone who chose Alpha? Again: raise the Alpha's again.

  • Let me get this guy here. So why did you choose Alpha?

  • Student: You would minimize your losses;

  • you'd get 0 or -1 instead of -3 or 1.

  • Professor Ben Polak: All right, so this gentleman is

  • saying - Student: There's no dominant strategy so -

  • Professor Ben Polak: Right,

  • so this gentleman's saying, a good reason for choosing

  • Alpha in this game is it's less risky.

  • The worst case scenario is less bad, is a way of saying it.

  • What about somebody who chose Beta?

  • A lot of you chose Beta. Let's have a show of hands on

  • the Beta's again. Let me see the Beta's again.

  • So, raise your hands. Can we get the woman here?

  • Can we ask her why she chose Beta?

  • Student: Because if you choose Alpha,

  • the best case scenario is you get 0,

  • so that's - Professor Ben Polak: Okay good,

  • that's a good counter argument. So the gentleman here was

  • looking at the worst case scenario, and the woman here was

  • looking at the best case scenario.

  • And the best case scenario here looks like getting a 1 here.

  • Now, let's ask a different question.

  • Is one of the strategies dominated in this game?

  • No, neither strategy is dominated.

  • Let's just check. If my pair chooses Alpha,

  • then my choosing Alpha yields 0, Beta -3: so Alpha would be

  • better. But if my pair chooses Beta

  • then Alpha yields -1, Beta yields 1:

  • in this case Beta would be better.

  • So Alpha in this case is better against Alpha,

  • and Beta is better against Beta, but neither dominates each

  • other. So here's a game where we just

  • change the payoffs. We have the same basic

  • structure, the same outcomes, but we imagine people cared

  • about different things and we end up with a very different

  • answer. In the first game,

  • it was kind of clear that we should choose Alpha and here

  • it's not at all clear what we can do--what we should do.

  • In fact, this kind of game has a name and we'll revisit it

  • later on in the semester. This kind of game is called a

  • "coordination problem." We'll talk about coordination

  • problems later on. The main lesson I want to get

  • out of this for today, is a simpler lesson.

  • It's the lesson that payoffs matter.

  • We change the payoffs, we change what people cared

  • about, and we get a very different game with a very

  • different outcome. So the basic lesson is that

  • payoffs matter, but let me say it a different

  • way. So without giving away my age

  • too much--I guess it will actually--when I was a kid

  • growing up in England, there was this guy - there was

  • a pop star--a slightly post-punk pop star called Joe Jackson,

  • who none of you would have heard of, because you were all

  • about ten years old, my fault.

  • And Joe Jackson had this song which had the lyric,

  • something like, you can't get what you want

  • unless you know what you want.

  • As a statement of logic, that's false.

  • It could be that what you want just drops into your lap without

  • you knowing about it. But as a statement of strategy,

  • it's a pretty good idea. It's a good idea to try and

  • figure out what your goals are--what you're trying to

  • achieve--before you go ahead and analyze the game.

  • So payoffs matter. Let's put it in his version.

  • "You can't get what you want, till you know what you want."

  • Be honest, how many of you have heard of Joe Jackson?

  • That makes me feel old, oh man, okay.

  • Goes down every year. So far we've looked at this

  • game as played by people who are evil gits, and we've looked at

  • this game as played by people who are indignant angels.

  • But we can do something more interesting.

  • We can imagine playing this game on a sort of mix and match.

  • For example, imagine--this shouldn't be hard

  • for most of you--imagine that you are an evil git,

  • but you know that the person you're playing against is an

  • indignant angel. So again, imagine that you know

  • you're an evil git, but you know that the person

  • you're playing against or with, is an indignant angel.

  • What should you do in that case? What should we do?

  • Who thinks you should choose Alpha in that case?

  • Let's pan the room again if we can.

  • Keep your hands up so that you can see.

  • Who thinks you should choose Beta in that case?

  • Who's abstaining here? Not allowed to abstain in this

  • class: it's a complete no-no. Okay, we'll allow some

  • abstention in the first day but not beyond today.

  • Let's have a look. Let's analyze this combined

  • game. So what does this game look

  • like? It's an evil git versus an

  • indignant angel and we can put the payoff matrix together by

  • combining the matrices we had before.

  • So in this case, this is me as always.

  • This is my pair, the column player.

  • My payoffs are going to be what? My payoffs are going to be

  • evil-git payoffs, so they come from the matrix up

  • there. So if someone will just help me

  • reading it off there. That's a 0, a 3,a -1, and a 1.

  • My opponent or my partner's payoffs come from the indignant

  • angel matrix. So they come from here.

  • There's a 0, a -3, a -1, and a 1.

  • Everyone see how I constructed that?

  • So just to remind you again, the first payoff is the row

  • player's payoff, in this case the evil git.

  • And the second payoff is the column player's payoff,

  • in this case the indignant angel.

  • Now we've set it up as a matrix, let's try again that

  • question I asked before. Suppose you're the row player

  • here. You're the evil git.

  • Those are your payoffs. You're playing against an

  • indignant angel, what would you do?

  • So once again, no abstentions this time:

  • who would choose Alpha? Let's have a show of hands

  • again, keep your hands up a second.

  • Who would choose Beta? Very few Beta's,

  • but mostly Alpha's. Alpha, I think,

  • is the right answer here but why?

  • Why is Alpha the right answer here?

  • Yeah, can we get this guy here? Student: It's the

  • dominant strategy. Professor Ben Polak:

  • Good. Actually nothing has changed

  • from the game we started with. The fact that I changed the

  • other guy's payoffs didn't matter here.

  • Alpha was dominant before--it dominated Beta before--and it

  • still dominates Beta. Let's just check.

  • If my opponent chooses Alpha and I choose Alpha,

  • I get 0; Beta, I get -1.

  • So Alpha would be better. If my opponent chooses Beta and

  • I choose Alpha, I get 3;

  • Beta, I get 1. Once again Alpha is better.

  • So as before, Alpha does better than Beta for

  • me, regardless of what the other person does.

  • Alpha dominates Beta. What was the first lesson of

  • the class? Shout it out please.

  • Right, so you should all have been choosing in this game,

  • you all should have chosen Alpha.

  • So the one person who didn't we'll let him off for today.

  • So Alpha dominates Beta here. Let's flip things around.

  • Suppose now--harder to imagine, but let's try it--suppose now

  • that you are an indignant angel and you're playing against,

  • and you know this, you're playing against an evil

  • git. You're an indignant angel,

  • so you have the payoffs that are still there and you're

  • playing against an evil git, which is the payoffs we covered

  • up but we'll reproduce them. Let's produce that matrix.

  • By the way, if this is beginning to sound like a

  • wrestling match, I don't mean it to.

  • Let's try here: Alpha, Beta,

  • Alpha, Beta, pair, me.

  • So my payoffs this time, are the indignant angel

  • payoffs. So mine are 0, -1, -3, and 1.

  • And my opponent's payoffs are what would have been my payoffs

  • before. They come from the other matrix.

  • Let's just show you it. They come from this matrix.

  • So they're going to be 0, -1,3, 1.

  • I took the second payoff from that matrix and made it the

  • second payoff in this matrix. Everyone see how I did that?

  • Once again, the row player is the first payoff and the column

  • player is the other payoff. What should you do in this case?

  • You're the indignant angel. You're playing against this

  • evil git. What should you do?

  • Write down on your notepad what you should do.

  • Show it to your neighbor so you can't cheat, or you can cheat

  • but you'll be shamed in front of your neighbor.

  • Raise your hands. Let Jude see it.

  • Raise your hands and keep them up if you chose Alpha now.

  • How about if you chose Beta now? So one or two Beta's,

  • mostly Alpha's. Well let's see.

  • Let's reason this through a second.

  • Does my Alpha dominate my Beta? No, in fact,

  • Alpha doesn't dominate Beta for me.

  • It doesn't dominate Beta. If my pair chooses Alpha then

  • Alpha gets me 0; Beta -3.

  • So Alpha does better. But if my pair chooses Beta,

  • then Alpha gets me -1; Beta gets me 1.

  • In this case Beta is better. As we saw before,

  • Alpha is better against Alpha. Beta is better against Beta.

  • There's no dominance going on here.

  • Nevertheless, at least 90% of you chose Alpha

  • here, and that's the right answer.

  • Why? Why should you choose Alpha

  • here? Somebody

  • can we get the guy with the beard here?

  • Wait for the mike, great. Student: We had

  • acknowledged that Alpha is a dominant strategy for my

  • opponent so we must choose based upon,

  • or knowing that my partner is going to choose Alpha.

  • Professor Ben Polak: Good, and your name is?

  • Student: Henry. Professor Ben Polak:

  • Henry. So Henry is saying sure I don't

  • have a dominated strategy. My Alpha doesn't dominate my

  • Beta. But look at my opponent.

  • My opponent's Alpha dominates her Beta.

  • If I choose Alpha and she chooses Alpha to get 0;

  • Beta she gets -1. Alpha is better.

  • If I choose Beta, if she chooses Alpha she gets

  • 3; Beta 1.

  • Again Alpha is better. For my opponent,

  • Alpha dominates Beta. So by thinking about my

  • opponent, by putting myself in my opponent's shoes,

  • I realize that she has a dominant strategy,

  • Alpha. She's going to choose Alpha and

  • my best response against Alpha is to choose Alpha myself.

  • So here, this time, my Alpha does not dominate Beta

  • but my pair's choice of Alpha dominates her choice,

  • her possible choice of Beta. So she will choose Alpha.

  • And once I know that she's going to choose Alpha,

  • it's clear that I should choose Alpha and get 0 rather than Beta

  • and get -3. So I should choose Alpha also.

  • Okay, so now we've seen four different combinations.

  • We've seen a case where an evil git was playing an evil git;

  • where an indignant angel was playing an indignant angel;

  • and we've seen both the flips of those: the evil git versus

  • the indignant angel; and the indignant angel against

  • the evil git. Why are we doing this?

  • Because there's an important lesson here.

  • What's the lesson here? The lesson is--comes from this

  • game--that a great way to analyze games,

  • a great way to get used to the idea of strategic thinking,

  • perhaps even the essence of strategic thinking,

  • is the ability to put yourself in someone else's shoes,

  • figure out what their payoffs are, and try and figure out what

  • they're going to do. So the big lesson of this game

  • is--I forgot what number we're up too--I guess this is Lesson 4

  • I think. Lesson 4 is:

  • put yourself in others' shoes and try to figure out what they

  • will do. In a sense, this is the first

  • difficult lesson of the class. It's easy to spot when a

  • strategy is dominant, more or less.

  • It's pretty easy to figure out, you have to know about your own

  • payoffs. But the hard thing in life,

  • is getting you to come out of your own selves a bit,

  • realizing it's "not all about you."

  • You've got to put yourself in other people's shoes to figure

  • out what they care about and what they're going to try and

  • do, so you can respond well to that.

  • While we're here, let's just mention that things

  • will get more complicated in a world where I don't actually

  • know the payoffs of my opponent. It's much easier to figure out

  • my own payoffs than to figure out my opponent's payoffs.

  • I might not know whether I'm playing someone who's an evil

  • git or an indignant angel. So I'm going to have to figure

  • out what the odds are of that in doing this exercise.

  • And we're going to come back to that idea too way at the end of

  • the class, but that's getting a bit ahead of ourselves,

  • but we'll get there. Now, it turns out that this

  • game, this Prisoner's Dilemma, with the Alpha's and Beta's,

  • or essentially the same game, has been played many,

  • many, many times in experiments.

  • So out there in the real world--I think we can do this

  • here--out there in the real world when they do these

  • experiments, they find out that roughly 70%

  • of people choose Alpha and roughly 30% choose Beta.

  • Roughly, almost a third choose Beta.

  • What do we think is going on? That's a third of the people

  • who seem to be choosing a dominated strategy

  • or is it? What's going on there?

  • Why do you think 30% of people are choosing Beta?

  • Anybody? Can we catch this guy here?

  • Student: They might be motivated by the fact that every

  • person who chooses Beta raises the average score.

  • Professor Ben Polak: They could be moral people.

  • So one possibility is: this 30% of people in the real

  • world who choose Beta are just nice people.

  • What else could it be? Yeah?

  • Student: I know this might be changing the game a

  • little bit, but if you ever expected to play the same game

  • with the partner you have more [inaudible]

  • Professor Ben Polak: All right,

  • they could be thinking they're going to play again.

  • Student: [inaudible] long run payoffs are greater if

  • you choose Beta every time. Professor Ben Polak: So

  • it could be that they think that this is actually--they haven't

  • understood the experiment and they think this is a multi shot

  • game, not a one shot game, good.

  • What else could it be? What's the simplest explanation?

  • What's the other obvious explanation?

  • They could just be stupid, right?

  • It could be., Are we allowed to say that in

  • class? Let's be honest here,

  • when we say experiments in the real world in Game Theory--or

  • the ones you read about in The New York Times--the real world

  • when it comes to experiments in Economics really means

  • undergraduates at the University of Arizona.

  • I mean, I'm not making it up. It just does.

  • They all are. I don't know anything about

  • are any of you from Arizona, I don't know.

  • I don't know whether the average undergrad at the

  • University of Arizona just has a sunny personality or whether

  • they "spent too long in the sun."

  • I just don't know which it is, right?

  • We can't really distinguish from this.

  • How about at Yale. What's our numbers here.

  • How about in this class? Do you want to mike your

  • colleague here? So 238 at Yale--this is

  • Yale--versus 36. So even at my level of

  • arithmetic that's a lot less than 30%.

  • That's more like less than 15%. It's about 15% I guess.

  • So 236--I'm sorry 238--chose Alpha, and 36 chose Beta.

  • Now there's one more lesson in this class and this is going to

  • be it. This isn't the end of the class

  • but one more lesson to take home.

  • You guys are going to be playing games among each other

  • today and until--whatever it is?--December 7,

  • whatever is the end of term. Look around each other.

  • You better get to know each other a bit.

  • And what did we learn today about you guys?

  • The lesson here, Lesson 5, is "Yale students are

  • evil." Be aware of that when you're playing games.

  • I want to play one more game today in the remaining minutes.

  • It doesn't matter if we finish a little bit early,

  • but I want to try to get this game at least started.

  • So do you all have Game #2 in front of you?

  • Just while you're reading that over, can I also make sure

  • you've all got your legal forms and you're going to sign.

  • Don't walk away with your legal forms, we need to get those

  • collected in. So at the end of talking about

  • this game, I'm going to collect in both the second game for the

  • class and also the legal form. If you don't have a legal form,

  • if you've lost it or something, it's online.

  • Let's have a look at that second game.

  • I'll read it out for you. Game 2: "pick a number."

  • Everyone got this? Anyone not got this?

  • Everyone got it? Good.

  • "Without showing your neighbor what you're doing,

  • put in the box below a whole number between 1 and a 100

  • [whole number between 1 and 100--integer.]

  • We will calculate the average number chosen in the class.

  • The winner in this game is the person whose number is closest

  • to two-thirds times the average in the class."

  • [Again: the winner is the person whose number is closest

  • to two-thirds times the average number in the class.]

  • The winner will win $5 minus the difference in pennies

  • between her choice and that two-thirds of the average."

  • Just to make sure you've understood this,

  • let me do an example on the board.

  • I've got one more board; that's good.

  • So imagine there were three people in the class,

  • and imagine that they chose 25,5, and 60.

  • So 25 plus 5 plus 60 is 90. People should feel free to

  • correct my arithmetic because it's often wrong;

  • 90 right? Two-thirds of 90,

  • whoops, what do I need, start again.

  • I need to divide it by three to get the average.

  • So the average is 30. So the total is 90,

  • the average is 30, am I right so far?

  • So two-thirds of the average is 20.

  • I'm looking desperately at the T.A.

  • Is that right? Okay, so the average is 30 and

  • two-thirds of the average is 20. So who's the winner here,

  • which number would have won here?

  • 25 would have won. 25 would have been the closest,

  • and what would they have won? They would have won five bucks

  • minus five cents for a total of four ninety-five.

  • Now to make this interesting, let's play this for real.

  • So this of course relies on me having brought some money and

  • we'll have to do this without dislodging the microphone.

  • So I'm going to see if I havesorry about that.

  • I'm going to see if I have enough money to do this in class

  • for real. When we played this game in the

  • old days, during the dot com boom with the MBA students,

  • you had to put fifty dollars on the table to get them

  • interested. Graduate students:

  • five cents will do it. Okay, so this is a--there's

  • some bloke with a beard on this one.

  • Yeah this is Lincoln apparently. Who knew, Lincoln?

  • Okay, so this is a five-dollar note and I'm going to put

  • it--sorry about that again--I'm going to put it in an envelope.

  • I'm not cheating anybody? No magic tricks here.

  • And this is going to be the prize for this game and we

  • better give this to someone we trust.

  • It's the prize for 159.Who do you guys trust?

  • The camera guy. Okay Jude: we know Jude's going

  • to be there next week. I'm giving it to Jude.

  • You can't see this on camera.--people at home--but I'm

  • giving it to Jude okay. I'm going to put it here,

  • and Jude has to show up next week with the prize.

  • I thought we should give it to the guy at the back,

  • who is the moral guy. Who is our moral guy at the

  • back? Well never mind,

  • we will give it to Jude. We know Jude's going to be here.

  • All right, has everyone put a number down?

  • Any questions? Just shout them out to me.

  • Student: So given that we only have one five dollar

  • bill does there have to be one unique winner,

  • and if so, how is that determined if we have multiple

  • people who are - Professor Ben Polak: That's a good

  • question. If there's multiple winners,

  • we'll divide it but we'll make sure everyone has a positive

  • winning. Good question.

  • Given the number of people in the room there may be multiple

  • winners, I accept that possibility.

  • Has everyone written down a number now?

  • All right, so hand your numbers to the end of the row,

  • but don't go yet. Hand it on to the end of the

  • row. Before you go I want five

  • things from you. I want to know the five lessons

  • from this class. Tell me what you learnt?

  • What were the five lessons? Without looking at your notes,

  • what were the five lessons? Anybody, shout out one of the

  • lessons, yes madam. Student: Don't play a

  • strictly dominated strategy. Professor Ben Polak:

  • Don't play a strictly dominated strategy, anything else?

  • Yes sir. Student: Yale students

  • are evil. Professor Ben Polak:

  • Yale students are evil. Two lessons down, three to go.

  • The guy over here. Student: Rational

  • choices can lead to bad outcomes.

  • Professor Ben Polak: Rational choices can lead to bad

  • outcomes. We put it more graphically

  • before but that's fine. Two more outcomes.

  • Student: Put yourself in other people's shoes.

  • Professor Ben Polak: Put yourself in other people's shoes

  • and I'm missing one, I can't recall which one I'm

  • missing now. Student: You can't get

  • what you want so you - Professor Ben Polak: You

  • can't get what you want. You could but it's a good idea

  • to figure out what you want before you try and get what you

  • want. Five things you learnt today,

  • hand in your numbers and the legal forms and I'll see you on

  • Monday.

Professor Ben Polak: So this is Game Theory Economics

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1.イントロダクション:5つの最初のレッスン (1. Introduction: five first lessons)

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    吴学志 に公開 2021 年 01 月 14 日
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