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1. Introduction: five first lessons — Transcript

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0:02Professor Ben Polak: So this is Game Theory Economics
0:04159. If you're here for art history,
0:06you're either in the wrong room or stay anyway,
0:08maybe this is the right room; but this is Game Theory, okay.
0:12You should have four handouts; everyone should have four
0:16handouts. There is a legal release
0:18form--we'll talk about it in a minute--about the videoing.
0:21There is a syllabus, which is a preliminary
0:23syllabus: it's also online. And there are two games labeled
0:27Game 1 and Game 2. Can I get you all to look at
0:31Game 1 and start thinking about it.
0:33And while you're thinking about it, I am hoping you can
0:36multitask a bit. I'll describe a bit about the
0:38class and we'll get a bit of admin under our belts.
0:40But please try and look at--somebody's not looking at
0:43it, because they're using it as a fan here--so look at Game 1
0:45and fill out that form for me, okay?
0:49So while you're filling that out, let me tell you a little
0:51bit about what we're going to be doing here.
0:53So what is Game Theory? Game Theory is a method of
0:57studying strategic situations. So what's a strategic situation?
1:02Well let's start off with what's not a strategic
1:04situation. In your Economics - in your
1:06Intro Economics class in 115 or 110, you saw some pretty good
1:09examples of situations that were not strategic.
1:12You saw firms working in perfect competition.
1:16Firms in perfect competition are price takers:
1:18they don't particularly have to worry about the actions of their
1:22competitors. You also saw firms that were
1:24monopolists and monopolists don't have any competitors to
1:26worry about, so that's not a particularly strategic
1:28situation. They're not price takers but
1:30they take the demand curve. Is this looking familiar for
1:33some of you who can remember doing 115 last year or maybe two
1:36years ago for some of you? Everything in between is
1:39strategic. So everything that constitutes
1:42imperfect competition is a strategic setting.
1:45Think about the motor industry, the motor car industry.
1:47Ford has to worry about what GM is doing and what Toyota is
1:50doing, and for the moment at least what Chrysler is doing but
1:54perhaps not for long. So there's a small number of
1:57firms and their actions affect each other.
1:59So for a literal definition of what strategic means:
2:02it's a setting where the outcomes that affect you depend
2:06on actions, not just on your own actions,
2:09but on actions of others. All right, that's as much as
2:12I'm going to say for preview right now, we're going to come
2:14back and see plenty of this over the course of the next semester.
2:16So what I want to do is get on to where this applies.
2:19It obviously applies in Economics, but it also applies
2:22in politics, and in fact, this class will count as a
2:25Political Science class if you're a Political Science
2:27major. You should go check with the
2:30DUS in Political Science. It count - Game Theory is very
2:34important in law these days. So for those of you--for the
2:37half of you--that are going to end up in law school,
2:39this is pretty good training. Game Theory is also used in
2:42biology and towards the middle of the semester we're actually
2:45going to see some examples of Game Theory as applied to
2:48evolution. And not surprisingly,
2:51Game Theory applies to sport. So let's talk about a bit of
2:57admin. How are you doing on filling
2:58out those games? Everyone managing to multitask:
3:00filling in Game 1? Keep writing.
3:03I want to get some admin out of the way and I want to start by
3:05getting out of the way what is obviously the elephant in the
3:07room. Some of you will have noticed
3:10that there's a camera crew here, okay.
3:12So as some of you probably know, Yale is undergoing an open
3:17education project and they're videoing several classes,
3:22and the idea of this, is to make educational
3:25materials available beyond the walls of Yale.
3:28In fact, on the web, internationally,
3:30so people in places, maybe places in the U.S.
3:32or places miles away, maybe in Timbuktu or whatever,
3:35who find it difficult to get educational materials from the
3:39local university or whatever, can watch certain lectures from
3:44Yale on the web. Some of you would have been in
3:47classes that do that before. What's going to different about
3:49this class is that you're going to be participating in it.
3:53The way we teach this class is we're going to play games,
3:55we're going to have discussions,
3:56we're going to talk among the class, and you're going to be
3:59learning from each other, and I want you to help people
4:03watching at home to be able to learn too.
4:06And that means you're going to be on film, at the very least on
4:09mike. So how's that going to work?
4:11Around the room are three T.A.s holding mikes.
4:14Let me show you where they are: one here, one here,
4:17and one here. When I ask for classroom
4:19discussions, I'm going to have one of the T.A.s go to you with
4:24a microphone much like in "Donahue" or something,
4:27okay. At certain times,
4:29you're going to be seen on film, so the camera is actually
4:31going to come around and point in your direction.
4:33Now I really want this to happen.
4:35I had to argue for this to happen, cause I really feel that
4:38this class isn't about me. I'm part of the class
4:40obviously, but it's about you teaching each other and
4:43participating. But there's a catch,
4:45the catch is, that that means you have to
4:47sign that legal release form. So you'll see that you have in
4:50front of you a legal release form, you have to be able to
4:52sign it, and what that says is that we
4:54can use you being shown in class.
4:56Think of this as a bad hair day release form.
4:59All right, you can't sue Yale later if you had a bad hair day.
5:03For those of you who are on the run from the FBI,
5:06your Visa has run out, or you're sitting next to your
5:09ex-girlfriend, now would be a good time to put
5:12a paper bag over your head. All right, now just to get you
5:15used to the idea, in every class we're going to
5:18have I think the same two people, so Jude is the
5:20cameraman; why don't you all wave to Jude:
5:24this is Jude okay. And Wes is our audio guy:
5:27this is Wes. And I will try and remember not
5:29to include Jude and Wes in the classroom discussions,
5:32but you should be aware that they're there.
5:34Now, if this is making you nervous, if it's any
5:36consolation, it's making me very nervous.
5:37So, all right, we'll try and make this class
5:40work as smoothly as we can, allowing for this extra thing.
5:43Let me just say, no one's making any money off
5:45this--at least I'm hoping these guys are being paid--but me and
5:48the T.A.s are not being paid. The aim of this,
5:50that I think is a good aim, it's an educational project,
5:53and I'm hoping you'll help us with it.
5:55The one difference it is going to mean, is that at times I
5:58might hold some of the discussions for the class,
6:00coming down into this part of the room, here,
6:04to make it a little easier for Jude.
6:07All right, how are we doing now on filling out those forms?
6:09Has everyone filled in their strategy for the first game?
6:13Not yet. Okay, let's go on doing a bit
6:16more admin. The thing you mostly care about
6:18I'm guessing, is the grades.
6:19All right, so how is the grade going to work for this class?
6:2230% of the class will be on problem sets,
6:2530% of the grade; 30% on the mid-term,
6:28and 40% on the final; so 30/30/40.
6:31The mid-term will be held in class on October 17^(th);
6:36that is also in your syllabus. Please don't anybody tell me
6:39late - any time after today you didn't know when the mid-term
6:42was and therefore it clashes with 17 different things.
6:45The mid-term is on October 17^(th), which is a Wednesday,
6:50in class. All right, the problem sets:
6:53there will be roughly ten problem sets and I'll talk about
6:56them more later on when I hand them out.
6:59The first one will go out on Monday but it will be due ten
7:03days later. Roughly speaking they'll be
7:05every week. The grade distribution:
7:06all right, so this is the rough grade distribution.
7:09Roughly speaking, a sixth of the class are going
7:11to end up with A's, a sixth are going to end up
7:14with A-, a sixth are going to end up
7:15with B+, a sixth are going to end up with B,
7:17a sixth are going to end up with B-,
7:19and the remaining sixth, if I added that up right,
7:21are going to end up with what I guess we're now calling the
7:24presidential grade, is that right?
7:27That's not literally true. I'm going to squeeze it a bit,
7:31I'm going to curve it a bit, so actually slightly fewer than
7:34a sixth will get straight A's, and fewer than a sixth will get
7:38C's and below. We'll squeeze the middle to
7:40make them be more B's. One thing I can guarantee from
7:44past experience in this class, is that the median grade will
7:47be a B+. The median will fall somewhere
7:51in the B+'s. Just as forewarning for people
7:54who have forgotten what a median is, that means half of you--not
7:57approximately half, it means exactly half of
8:00you--will be getting something like B+ and below and half will
8:04get something like B+ and above. Now, how are you doing in
8:07filling in the forms? Everyone filled them in yet?
8:09Surely must be pretty close to getting everyone filled in.
8:12All right, so last things to talk about before I actually
8:15collect them in - textbooks. There are textbooks for this
8:19class. The main textbook is this one,
8:21Dutta's book Strategy and Games.
8:24If you want a slightly tougher book, more rigorous book,
8:28try Joel Watson's book, Strategies.
8:30Both of those books are available at the bookstore.
8:33But I want to warn everybody ahead of time,
8:36I will not be following the textbook.
8:38I regard these books as safety nets.
8:40If you don't understand something that happened in
8:43class, you want to reinforce an idea that came up in class,
8:45then you should read the relevant chapters in the book
8:48and the syllabus will tell you which chapters to read for each
8:50class, or for each week of class,
8:52all right. But I will not be following
8:54these books religiously at all. In fact, they're just there as
8:58back up. In addition,
8:59I strongly recommend people read, Thinking
9:03Strategically. This is good bedtime reading.
9:06Do any of you suffer from insomnia?
9:08It's very good bedtime reading if you suffer from insomnia.
9:12It's a good book and what's more there's going to be a new
9:14edition of this book this year and Norton have allowed us to
9:17get advance copies of it. So if you don't buy this book
9:20this week, I may be able to make the advance copy of the new
9:24edition available for some of you next week.
9:26I'm not taking a cut on that either, all right,
9:29there's no money changing hands.
9:31All right, sections are on the syllabus sign up - sorry on the
9:34website, sign up as usual. Put yourself down on the wait
9:36list if you don't get into the section you want.
9:38You probably will get into the section you want once we're
9:40done. All right, now we must be done
9:41with the forms. Are we done with the forms?
9:43All right, so why don't we send the T.A.s, with or without
9:46mikes, up and down the aisles and collect in your Game #1;
9:50not Game #2, just Game #1.
10:05Just while we're doing that, I think the reputation of this
10:08class--I think--if you look at the course evaluations online or
10:11whatever, is that this class is
10:14reasonably hard but reasonably fun.
10:17So I'm hoping that's what the reputation of the class is.
10:20If you think this class is going to be easy,
10:22I think it isn't actually an easy class.
10:24It's actually quite a hard class, but I think I can
10:27guarantee it's going to be a fun class.
10:29Now one reason it's a fun class, is the nice thing about
10:32teaching Game Theory - quieten down folks--one thing about
10:35teaching Game Theory is, you get to play games,
10:38and that's exactly what we've just been doing now.
10:40This is our first game and we're going to play games
10:46throughout the course, sometimes several times a week,
10:51sometimes just once a week. We got all these things in?
10:56Everyone handed them in? So I need to get those counted.
11:08Has anyone taken the Yale Accounting class?
11:12No one wants to - has aspirations to be - one person
11:15has. I'll have a T.A.
11:15do it, it's all right, we'll have a T.A.
11:17do it. So Kaj, can you count those for
11:19me? Is that right?
11:23Let me read out the game you've just played.
11:25"Game 1, a simple grade scheme for the class.
11:28Read the following carefully. Without showing your neighbor
11:32what you are doing, put it in the box below either
11:34the letter Alpha or the letter Beta.
11:37Think of this as a grade bid. I will randomly pair your form
11:42with another form and neither you nor your pair will ever know
11:46with whom you were paired. Here's how the grades may be
11:49assigned for the class. [Well they won't be,
11:52but we can pretend.] If you put Alpha and you're
11:55paired with Beta, then you will get an A and your
11:57pair a C. If you and your pair both put
12:00Alpha, you'll both get B-. If you put Beta and you're
12:03paired with Alpha, you'll get a C and your pair an
12:05A. If you and your pair both put
12:08Beta, then you'll both get B+." So that's the thing you just
12:11filled in. Now before we talk about this,
12:13let's just collect this information in a more useful
12:16way. So I'm going to remove this for
12:21now. We'll discuss this in a second,
12:25but why don't we actually record what the game is,
12:30that we're playing, first.
12:33So this is our grade game, and what I'm going to do,
12:36since it's kind of hard to absorb all the information just
12:40by reading a paragraph of text, I'm going to make a table to
12:44record the information. So what I'm going to do is I'm
12:47going to put me here, and my pair,
12:49the person I'm randomly paired with here,
12:52and Alpha and Beta, which are the choices I'm going
12:55to make here and on the columns Alpha and Beta,
12:58the choices my pair is making. In this table,
13:02I'm going to put my grades. So my grade if we both put
13:09Alpha is B-, if we both put Beta, was B+.
13:13If I put Alpha and she put a Beta, I got an A,
13:17and if I put Beta and she put an Alpha, I got a C.
13:21Is that correct? That's more or less right?
13:24Yeah, okay while we're here, why don't we do the same for my
13:29pair? So this is my grades on the
13:33left hand table, but now let's look at what my
13:39pair will do, what my pair will get.
13:45So I should warn the people sitting at the back that my
13:47handwriting is pretty bad, that's one reason for moving
13:49forward. The other thing I should
13:51apologize at this stage of the class is my accent.
13:54I will try and improve the handwriting, there's not much I
13:58can do about the accent at this stage.
14:02So once again if you both put Alpha then my pair gets a B-.
14:05If we both put Beta, then we both get a B+;
14:07in particular, my pair gets a B+.
14:09If I put Alpha and my pair puts Beta, then she gets a C.
14:14And if I put Beta and she puts Alpha, then she gets an A.
14:19So I now have all the information that was on the
14:22sheet of paper that you just handed in.
14:24Now there's another way of organizing this that's standard
14:27in Game Theory, so we may as well get used to
14:29it now on the first day. Rather then drawing two
14:31different tables like this, what I'm going to do is I'm
14:35going to take the second table and super-impose it on top of
14:39the first table. Okay, so let me do that and
14:42you'll see what I mean. What I'm going to do is draw a
14:45larger table, the same basic structure:
14:48I'm choosing Alpha and Beta on the rows,
14:51my pair is choosing Alpha and Beta on the columns,
14:55but now I'm going to put both grades in.
14:59So the easy ones are on the diagonal: you both get B- if we
15:04both choose Alpha; we both get B+ if we both
15:09choose Beta. But if I choose Alpha and my
15:13pair chooses Beta, I get an A and she gets a C.
15:18And if I choose Beta and she chooses Alpha,
15:21then it's me who gets the C and it's her who gets the A.
15:26So notice what I did here. The first grade corresponds to
15:29the row player, me in this case,
15:31and the second grade in each box corresponds to the column
15:35player, my pair in this case.
15:38So this is a nice succinct way of recording what was in the
15:41previous two tables. This is an outcome matrix;
15:44this tells us everything that was in the game.
15:53Okay, so now seems a good time to start talking about what
15:57people did. So let's just have a show of
15:59hands. How many of you chose Alpha?
16:04Leave your hands up so that Jude can catch that,
16:07so people can see at home, okay.
16:08All right and how many of you chose Beta?
16:12There's far more Alphas - wave your hands the Beta's okay.
16:16All right, there's a Beta here, okay.
16:17So it looks like a lot of - well we're going to find out,
16:19we're going to count--but a lot more Alpha's than Beta's.
16:21Let me try and find out some reasons why people chose.
16:24So let me have the Alpha's up again.
16:27So, the woman who's in red here, can we get a mike to the -
16:32yeah, is it okay if we ask you? You're not on the run from the
16:36FBI? We can ask you why?
16:37Okay, so you chose Alpha right? So why did you choose Alpha?
16:40Student: [inaudible] realized that my partner chose
16:45Alpha, therefore I chose [inaudible].
16:49Professor Ben Polak: All right, so you wrote out these
16:51squares, you realized what your partner was going to do,
16:53and responded to that. Any other reasons for choosing
16:56Alpha around the room? Can we get the woman here?
17:00Try not to be intimidated by these microphones,
17:02they're just mikes. It's okay.
17:05Student: The reason I chose Alpha, regardless of what
17:08my partner chose, I think there would be better
17:11outcomes than choosing Beta. Professor Ben Polak: All
17:14right, so let me ask your names for a second-so your name was?
17:16Student: Courtney. Professor Ben Polak:
17:18Courtney and your name was? Student: Clara Elise.
17:19Professor Ben Polak: Clara Elise.
17:19So slightly different reasons, same choice Alpha.
17:22Clara Elise's reason - what did Clara Elise say?
17:25She said, no matter what the other person does,
17:28she reckons she'd get a better grade if she chose Alpha.
17:31So hold that thought a second, we'll come back to - is it
17:33Clara Elise, is that right? We'll come back to Clara Elise
17:35in a second. Let's talk to the Beta's a
17:36second; let me just emphasize at this
17:38stage there are no wrong answers.
17:40Later on in the class there'll be some questions that have
17:41wrong answers. Right now there's no wrong
17:43answers. There may be bad reasons but
17:45there's no wrong answers. So let's have the Beta's up
17:47again. Let's see the Beta's.
17:49Oh come on! There was a Beta right here.
17:51You were a Beta right? You backed off the Beta, okay.
17:56So how can I get a mike into a Beta?
17:57Let' s stick in this aisle a bit.
17:58Is that a Beta right there? Are you a Beta right there?
18:01Can I get the Beta in here? Who was the Beta in here?
18:04Can we get the mike in there? Is that possible?
18:07In here - you can leave your hand so that - there we go.
18:09Just point towards - that's fine, just speak into it,
18:12that's fine. Student: So the reason
18:13right? Professor Ben Polak:
18:14Yeah, go ahead. Student: I personally
18:16don't like swings that much and it's the B-/B+ range,
18:18so I'd much rather prefer that to a swing from A to C,
18:22and that's my reason. Professor Ben Polak: All
18:25right, so you're saying it compresses the range.
18:27I'm not sure it does compress the range.
18:29I mean if you chose Alpha, you're swinging from A to B-;
18:34and from Beta, swinging from B+ to C.
18:37I mean those are similar kind of ranges but it certainly is a
18:40reason. Other reasons for choosing?
18:43Yeah, the guy in blue here, yep, good.
18:45That's all right. Don't hold the mike;
18:48just let it point at you, that's fine.
18:49Student: Well I guess I thought we could be more
18:53collusive and kind of work together, but I guess not.
18:56So I chose Beta. Professor Ben Polak:
19:00There's a siren in the background so I missed the
19:01answer. Stand up a second,
19:02so we can just hear you. Student: Sure.
19:03Professor Ben Polak: Sorry, say again.
19:04Student: Sure. My name is Travis.
19:05I thought we could work together, but I guess not.
19:08Professor Ben Polak: All right good.
19:10That's a pretty good reason. Student: If you had
19:12chosen Beta we would have all gotten B+'s but I guess not.
19:14Professor Ben Polak: Good, so Travis is giving us a
19:16different reason, right?
19:17He's saying that maybe, some of you in the room might
19:21actually care about each other's grades, right?
19:24I mean you all know each other in class.
19:26You all go to the same college. For example,
19:28if we played this game up in the business school--are there
19:32any MBA students here today? One or two.
19:36If we play this game up in the business school,
19:37I think it's quite likely we're going to get a lot of Alpha's
19:40chosen, right? But if we played this game up
19:42in let's say the Divinity School, all right and I'm
19:46guessing that Travis' answer is reflecting what you guys are
19:50reasoning here. If you played in the Divinity
19:53School, you might think that people in the Divinity School
19:55might care about other people's grades, right?
19:57There might be ethical reasons--perfectly good,
20:00sensible, ethical reasons--for choosing Beta in this game.
20:02There might be other reasons as well, but that's perhaps the
20:05reason to focus on. And perhaps,
20:07the lesson I want to draw out of this is that right now this
20:10is not a game. Right now we have actions,
20:12strategies for people to take, and we know what the outcomes
20:15are, but we're missing something that will make this a game.
20:18What are we missing here? Student: Objectives.
20:21Professor Ben Polak: We're missing objectives.
20:22We're missing payoffs. We're missing what people care
20:25about, all right. So we can't really start
20:27analyzing a game until we know what people care about,
20:29and until we know what the payoffs are.
20:31Now let's just say something now, which I'll probably forget
20:34to say in any other moment of the class, but today it's
20:36relevant. Game Theory,
20:38me, professors at Yale, cannot tell you what your
20:43payoff should be. I can't tell you in a useful
20:47way what it is that your goals in life should be or whatever.
20:51That's not what Game Theory is about.
20:53However, once we know what your payoffs are, once we know what
20:57your goals are, perhaps Game Theory can you
21:00help you get there. So we've had two different
21:03kinds of payoffs mentioned here. We had the kind of payoff where
21:06we care about our own grade, and Travis has mentioned the
21:08kind of payoff where you might care about other people's
21:11grades. And what we're going to do
21:14today is analyze this game under both those possible payoffs.
21:19To start that off, let's put up some possible
21:26payoffs for the game. And I promise we'll come back
21:31and look at some other payoffs later.
21:33We'll revisit the Divinity School later.
21:38All right, so here once again is our same matrix with me and
21:44my pair, choosing actions Alpha and Beta, but this time I'm
21:49going to put numbers in here. And some of you will perhaps
21:54recognize these numbers, but that's not really relevant
21:57for now. All right, so what's the idea
21:59here? Well the first idea is that
22:01these numbers represent utiles or utilities.
22:05They represent what these people are trying to maximize,
22:09what they're to achieve, their goals.
22:12The idea is - just to compare this to the outcome matrix - for
22:17the person who's me here, (A,C) yields a payoff of--(A,C)
22:23is this box--so (A,C) yields a payoff of three,
22:28whereas (B-,B-) yields a payoff of 0, and so on.
22:39So what's the interpretation? It's the first interpretation:
22:42the natural interpretation that a lot of you jumped to straight
22:44away. These are people--people with
22:46these payoffs are people--who only care about their own
22:50grades. They prefer an A to a B+,
22:52they prefer a B+ to a B-, and they prefer a B- to a C.
22:57Right, I'm hoping I the grades in order, otherwise it's going
23:00to ruin my curve at the end of the year.
23:02So these people only care about their own grades.
23:08They only care about their own grades.
23:16What do we call people who only care about their own grades?
23:18What's a good technical term for them?
23:22In England, I think we refer to these guys - whether it's
23:28technical or not - as "evil gits."
23:32These are not perhaps the most moral people in the universe.
23:37So now we can ask a different question.
23:39Suppose, whether these are actually your payoffs or not,
23:42pretend they are for now. Suppose these are all payoffs.
23:44Now we can ask, not what did you do,
23:47but what should you do? Now we have payoffs that can
23:49really switch the question to a normative question:
23:51what should you do? Let's come back to - was it
23:54Clara Elise--where was Clara Elise before?
23:57Let's get the mike on you again. So just explain what you did
24:00and why again. Student: Why I chose
24:02Alpha? Professor Ben Polak:
24:03Yeah, stand up a second, if that's okay.
24:04Student: Okay. Professor Ben Polak: You
24:06chose Alpha; I'm assuming these were roughly
24:08your payoffs, more or less,
24:08you were caring about your grades.
24:10Student: Yeah, I was thinking - Professor
24:11Ben Polak: Why did you choose Alpha?
24:12Student: I'm sorry? Professor Ben Polak: Why
24:13did you choose Alpha? Just repeat what you said
24:15before. Student: Because I
24:17thought the payoffs - the two different payoffs that I could
24:20have gotten--were highest if I chose Alpha.
24:22Professor Ben Polak: Good;
24:23so what Clara Elise is saying--it's an important
24:26idea--is this (and tell me if I'm paraphrasing you incorrectly
24:28but I think this is more or less what you're saying):
24:31is no matter what the other person does,
24:33no matter what the pair does, she obtains a higher payoff by
24:37choosing Alpha. Let's just see that.
24:40If the pair chooses Alpha and she chooses Alpha,
24:44then she gets 0. If the pair chooses Alpha and
24:48she chose Beta, she gets -1.
24:500 is bigger than -1. If the pair chooses Beta,
24:55then if she chooses Alpha she gets 3, Beta she gets 1,
24:59and 3 is bigger than 1. So in both cases,
25:01no matter what the other person does, she receives a higher
25:05payoff from choosing Alpha, so she should choose Alpha.
25:09Does everyone follow that line of reasoning?
25:11That's a stronger line of reasoning then the reasoning we
25:14had earlier. So the woman,
25:15I have immediately forgotten the name of, in the red shirt,
25:18whose name was - Student: Courtney.
25:20Professor Ben Polak: Courtney,
25:21so Courtney also gave a reason for choosing Alpha,
25:23and it was a perfectly good reason for choosing Alpha,
25:24nothing wrong with it, but notice that this reason's a
25:27stronger reason. It kind of implies your reason.
25:31So let's get some definitions down here.
25:35I think I can fit it in here. Let's try and fit it in here.
25:39Definition: We say that my strategy Alpha strictly
25:56dominates my strategy Beta, if my payoff from Alpha is
26:11strictly greater than that from Beta, [and this is the key
26:24part of the definition], regardless of what others
26:39do. Shall we just read that back?
26:44"We say that my strategy Alpha strictly dominates my strategy
26:48Beta, if my payoff from Alpha is strictly greater than that from
26:52Beta, regardless of what others do."
26:55Now it's by no means my main aim in this class to teach you
26:59jargon. But a few bits of jargon are
27:01going to be helpful in allowing the conversation to move forward
27:03and this is certainly one. "Evil gits" is maybe one too,
27:08but this is certainly one. Let's draw out some lessons
27:12from this. Actually, so you can still read
27:15that, let me bring down and clean this board.
27:19So the first lesson of the class, and there are going to be
27:24lots of lessons, is a lesson that emerges
27:28immediately from the definition of a dominated strategy and it's
27:35this. So Lesson One of the course is:
27:44do not play a strictly dominated strategy.
27:58So with apologies to Strunk and White, this is in the passive
28:02form, that's dominated, passive voice.
28:04Do not play a strictly dominated strategy.
28:10Why? Somebody want to tell me why?
28:15Do you want to get this guy? Stand up - yeah.
28:20Student: Because everyone's going to pick the
28:23dominant outcome and then everyone's going to get the
28:26worst result - the collectively worst result.
28:28Professor Ben Polak: Yeah, that's a possible answer.
28:30I'm looking for something more direct here.
28:31So we look at the definition of a strictly dominated strategy.
28:34I'm saying never play one. What's a possible reason for
28:37that? Let's - can we get the woman
28:40there? Student: [inaudible]
28:41Professor Ben Polak: "You'll always lose."
28:43Well, I don't know: it's not about winning and
28:45losing. What else could we have?
28:46Could we get this guy in the pink down here?
28:50Student: Well, the payoffs are lower.
28:51Professor Ben Polak: The payoffs are lower,
28:53okay. So here's an abbreviated
28:55version of that, I mean it's perhaps a little
28:58bit longer. The reason I don't want to play
29:01a strictly dominated strategy is, if instead,
29:05I play the strategy that dominates it,
29:08I do better in every case. The reason I never want to play
29:11a strictly dominated strategy is, if instead I play the
29:14strategy that dominates it, whatever anyone else does I'm
29:18doing better than I would have done.
29:21Now that's a pretty convincing argument.
29:23That sounds like a convincing argument.
29:24It sounds like too obvious even to be worth stating in class,
29:29so let me now try and shake your faith a little bit in this
29:33answer. You're somebody who's wanted by
29:36the FBI, right? Okay, so how about the
29:41following argument? Look at the payoff matrix again
29:46and suppose I reason as follows. Suppose I reason and say if we,
29:51me and my pair, both reason this way and choose
29:54Alpha then we'll both get 0. But if we both reasoned a
29:58different way and chose Beta, then we'll both get 1.
30:01So I should choose Beta: 1 is bigger than 0,
30:04I should choose Beta. What's wrong with that argument?
30:08My argument must be wrong because it goes against the
30:10lesson of the class and the lessons of the class are gospel
30:12right, they're not wrong ever,
30:13so what's wrong with that argument?
30:15Yes, Ale - yeah good. Student: Well because
30:21you have to be able to agree, you have to be able to speak to
30:23them but we aren't allowed to show our partners what we wrote.
30:25Professor Ben Polak: All right, so it involves some
30:29notion of agreeing. So certainly part of the
30:31problem here, with the reasoning I just gave
30:33you--the reasoning that said I should choose Beta,
30:35because if we both reason the same way, we both do better that
30:39way--involves some kind of magical reasoning.
30:41It's as if I'm arguing that if I reason this way and reason
30:44myself to choosing Beta, somehow I'm going to make the
30:48rest of you reason the same way too.
30:50It's like I've got ESP or I'm some character out of the X-Men,
30:53is that what it's called? The X-Men right?
30:56Now in fact, this may come as a surprise to
30:58you, I don't have ESP, I'm not a character out of the
31:00X-Men, and so you can't actually see
31:02brain waves emitting from my head, and my reasoning doesn't
31:05affect your reasoning. So if I did reason that way,
31:08and chose Beta, I'm not going to affect your
31:11choice one way or the other. That's the first thing that's
31:14wrong with that reasoning. What else is wrong with that
31:16reasoning? Yeah, that guy down here.
31:20Student: Well, the second that you choose Beta
31:22then someone's going - it's in someone's best interest to take
31:24advantage of it. Professor Ben Polak: All
31:25right, so someone's going to take advantage of me,
31:27but even more than that, an even stronger argument:
31:29that's true, but even a stronger argument.
31:30Well how about this? Even if I was that guy in the
31:33X-Men or the Matrix or whatever it was, who could reason his way
31:36into making people do things. Even if I could make everyone
31:40in the room choose Beta by the force of my brain waves,
31:44what should I then do? I should choose Alpha.
31:46If these are my payoffs I should go ahead and choose Alpha
31:49because that way I end up getting 3.
31:51So there's two things wrong with the argument.
31:54One, there's this magical reasoning aspect,
31:56my reasoning is controlling your actions.
31:58That doesn't happen in the real world.
32:00And two, even if that was the case I'd do better to myself
32:08choose Alpha. So, nevertheless,
32:11there's an element of truth in what I just said.
32:13It's the fact that there's an element of truth in it that
32:17makes it seem like a good argument.
32:19The element of truth is this. It is true that by both
32:23choosing Alpha we both ended up with B-'s.
32:27We both end up with payoffs of 0, rather than payoffs of 1.
32:32It is true that by both choosing, by both following this
32:35lesson and not choosing the dominated strategy Beta,
32:38we ended up with payoffs, (0,0), that were bad.
32:43And that's probably the second lesson of the class.
32:49So Lesson 2, and this lesson probably
32:51wouldn't be worth stating, if it wasn't for sort of a
32:55century of thought and economics that said the opposite.
32:59So rational choice [in this case, people not choosing a
33:02dominated strategy; people choosing a dominant
33:07strategy] rational choice can lead to
33:11outcomes that - what do Americans call this?--that
33:18"suck." If you want a more technical
33:22term for that (and you remember this from Economics 115),
33:25it can lead to outcomes that are "inefficient,"
33:27that are "Pareto inefficient," but "suck" will do for today.
33:30Rational choices by rational players, can lead to bad
33:35outcomes. So this is a famous example for
33:38this reason. It's a good illustration of
33:40this point. It's a famous example.
33:41What's the name of this example, somebody?
33:44This is called Prisoner's Dilemma.
33:46How many of you have heard of the Prisoner's Dilemma before?
33:48Most of you saw it in 115, why is it called the Prisoner's
33:53Dilemma? Yes, the guy here in orange.
33:57That's okay; he can just point at you that's
33:58fine. Student: I think it's
34:00whether or not the prisoner's cooperate in the sentence they
34:04have, and if they kind of rat out the
34:05other person, then they can have less;
34:07but if both rat out, then they like end up losing
34:10large scale. Professor Ben Polak:
34:12Good, so in the standard story you've got these two crooks,
34:15or two accused crooks, and they're in separate cells
34:18and they're being interviewed separately--kept apart--and
34:21they're both told that if neither of them rats the other
34:24guy out, they'll go to jail for say a
34:26year. If they both rat each other
34:28out, they'll end up in jail for two years, But if you rat the
34:31other guy out and he doesn't rat you out,
34:32then you will go home free and he'll go to jail for five years.
34:37Put that all down and you pretty quickly see that,
34:40regardless whether the other guy rats you or not,
34:42you're better off ratting him out.
34:44Now, if you have never seen that Prisoner's Dilemma,
34:47you can see it pretty much every night on a show called
34:51Law & Order. How many of you have seen
34:54Law & Order? If you haven't seen Law
34:56& Order, the way to see Law &
34:58Order is to go to a random TV set,
34:59at a random time, and turn on a random channel.
35:06This happens in every single episode, so much so that if any
35:08of you actually - I mean this might actually be true at
35:11Yale--but if you any of you or the TV guys: if any of you know
35:13the guy who writes the plots for this,
35:15have him come to the class (so I guess to see the video now)
35:18and we get some better plot lines in there.
35:20But, of course, that's not the only example.
35:23The grade game and this is not the only example.
35:25There are lots of examples of Prisoner's Dilemmas out there.
35:28Let's try and find some other ones.
35:30So how many of you have roommates in your college?
35:32How many of you have roommates? Most of you have roommates
35:36right? So I'm guessing now,
35:37I won't make you show your hands, because it's probably
35:40embarrassing, but what is the state of your
35:42dorm rooms, your shared dorm rooms, at the end of the
35:46semester or the end of the school year?
35:48So I'm just guessing, having been in a few of these
35:50things over the years, that by the end of the
35:52semester, or certainly by the end of the
35:54school year, the state of the average Yale dorm room is quite
35:57disgusting. Why is it disgusting?
36:02It's disgusting because people don't tidy up.
36:04They don't clean up those bits of pizza and bits of chewed
36:07bread and cheese, but why don't they tidy up?
36:09Well let's just work it out. What would you like to happen
36:12if you're sharing a dorm room? You'd like to have the other
36:15guy tidy up, right? The best thing for you is to
36:18have the other guy tidy up and the worst thing for you is to
36:21tidy up for the other guy. But now work it out:
36:23it's a Prisoner's Dilemma. If the other guy doesn't tidy
36:25up, you're best off not tidying up either, because the last
36:28thing you want is to be tidying up for the other guy.
36:30And if the other guy does tidy up, hey the room's clean,
36:33who cares? So either way,
36:34you're not going to tidy up and you end up with a typical Yale
36:36dorm room. Am I being unfair?
36:37Are your dorm rooms all perfect? This may be a gender thing but
36:41we're not going to go there. So there are lots of Prisoner's
36:45Dilemmas out there, anyone got any other examples?
36:48Other examples? I didn't quite hear that, sorry.
36:53Let's try and get a mike on it so we can really hear it.
36:55Student: [inaudible] Professor Ben Polak:
37:01Okay, in divorce struggles, okay.
37:05You're too young to be worrying about such things but never
37:07mind. Yeah, okay, that's a good
37:09example. All right, hiring lawyers,
37:11bringing in big guns. What about an Economics example?
37:15What about firms who are competing in prices?
37:18Both firms have an incentive to undercut the other firm,
37:22driving down profits for both. The last thing you want is to
37:25have the other firm undercut you, in an attempt to push
37:27prices down. That's good for us the
37:29consumers, but bad for the firm, bad for industry profit.
37:32What remedies do we see? We'll come back to this later
37:35on in the class, but let's have a preview.
37:36So what remedies do we see in society for Prisoner's Dilemmas?
37:40What kind of remedies do we see? Let me try and get the guy here
37:43right in front. Student: Collusion.
37:48Professor Ben Polak: Collusion;
37:48so firms could collude. So what prevents them from
37:55colluding? One thing they could do,
37:58presumably, is they could write a contract, these firms.
38:00They could say I won't lower my prices if you don't lower your
38:02prices, and they could put this contract in with the pricy
38:05lawyer, who's taking a day off from the
38:06divorce court, and that would secure that they
38:09wouldn't lower prices on each other.
38:10Is that right? So why wouldn't that work?
38:15Why wouldn't writing a contract here work?
38:19It's against the law. It's an illegal contract.
38:23What about you with your roommates?
38:24How many of you have a written contract, stuck with a magnet on
38:28the fridge, telling you, when you're supposed to tidy
38:31up. Very few of you.
38:32Why do you manage to get some cooperation between you and your
38:37roommates even without a written contract?
38:40Student: It's not legally enforceable.
38:42Professor Ben Polak: Well it probably is legally
38:43enforceable actually. This guy says not,
38:44but it probably is legally enforceable.
38:45He probably could have a written contract about tidying
38:48up. The woman in here.
38:50Student: Repetition; you do it over and over.
38:52Professor Ben Polak: Yeah, so maybe even among your
38:55roommates, maybe you don't need a contract because you can
38:58manage to achieve the same ends, by the fact that you're going
39:01to be interacting with the same person, over and over again
39:04during your time at Yale. So we'll come back and revisit
39:07the idea that repeating an interaction may allow you to
39:10obtain cooperation, but we're not going to come
39:12back to that until after the mid-term.
39:13That's way down the road but we'll get there.
39:16Now one person earlier on had mentioned something about
39:19communication. I think it was somebody in the
39:20front, right? So let's just think about this
39:22a second. Is communication the problem
39:24here? Is the reason people behave
39:26badly--I don't know "badly"--people choose Alpha in
39:28this game here, is it the fact that they can't
39:31communicate? Suppose you'd been able to talk
39:34before hand, so suppose the woman here whose name
39:36was…? Student: Mary.
39:37Professor Ben Polak: …Mary,
39:38had been able to talk to the person next to her whose name
39:39is…? Student: Erica.
39:40Professor Ben Polak: Erica.
39:41And they said, suppose we know we're going to
39:43be paired together, I'll choose Beta if you choose
39:45Beta. Would that work?
39:48Why wouldn't that work? Student: There's no
39:53enforcement. Professor Ben Polak:
39:54There's no enforcement. So it isn't a failure of
39:56communication per se. A contract is more then
40:00communication, a contract is communication
40:02with teeth. It actually changes the payoffs.
40:05So I could communicate with Alice on agreements,
40:07but back home I'm going to go ahead and choose Alpha anyway;
40:11all the better if he's choosing Beta.
40:13So we'll come back and talk about more of these things as
40:15the course goes on, but let's just come back to the
40:17two we forgot there: so the collusion case and the
40:20case back in Law & Order with the prisoners in the
40:23cell. How do they enforce their
40:25contracts? They don't always rat each
40:26other out and some firms manage to collude?
40:28How do they manage to enforce those contracts?
40:32Those agreements, how are they enforced?
40:34Student: They trust each other.
40:35Professor Ben Polak: It could be they trust each other,
40:37although if you trust a crook that's not…
40:39What else could it be? The guy here again with the
40:41beard, yeah. Student: Could be a zero
40:43sum game. Professor Ben Polak:
40:44Well, but this is the game. So here's the game.
40:45Student: No, but the pay,
40:47the way they value, the way of valuing each--
40:49Professor Ben Polak: Okay, so the payoffs may be
40:51different. I have something simpler in
40:53mind. Suppose they have a written
40:56contract, or even an unwritten contract, what enforces the
41:00contract for colluding firms or crooks in jail?
41:03Yeah. Student: Gets off Scott
41:05free in five years when the other guy gets out,
41:08he might run into a situation where [inaudible]
41:09Professor Ben Polak: Yeah,
41:11so a short version of that is, it's a different kind of
41:13contract. If you rat someone out in jail,
41:16someone puts a contract out on you.
41:18Tony Soprano enforces those contracts.
41:20That's the purpose of Tony Soprano.
41:22It's the purpose of the mafia. The reason the mafia thrives in
41:25countries where it's hard to write legal contracts--let's say
41:28some new parts of the former Soviet Union or some parts of
41:31Africa--the reason the mafia thrives in those environments,
41:34is that it substitutes for the law and enforces both legal and
41:39illegal contracts. So I promised a while ago now,
41:42that we were going to come back and look at this game under some
41:46other possible payoffs. So I wasn't under a contract
41:50but let's come back and fulfill that promise anyway.
41:54So we're going to revisit, if not the Divinity School,
41:58at least in people who have more morality than my friends up
42:03in the business school. We're going to ask for the same
42:07grade game we played at the beginning.
42:09What would happen if player's payoffs looked different?
42:19So these are "possible payoffs (2)."
42:22I'll give these a name.. We called the other guys "evil
42:25gits." We'll call these guys "indignant angels."
42:30I can never spell indignant.. Is that roughly right?
42:33Does that look right? I think it's right.
42:35In-dig-nant isn't it: indignant. Indignant angels,
42:37and we'll see why in a second. So here are their payoffs and
42:43once again the basic structure of the game hasn't changed.
42:51It's still I'm choosing Alpha and Beta, my pair is choosing
42:54Alpha and Beta, and the grades are the same as
42:56they were before. They're hidden by that board
42:59but you saw them before. But this time the payoffs are
43:02as follows. On the lead diagonal we still
43:05have (0,0) and (1,1). But now the grades here are
43:09-1--I'm sorry--the payoffs are -1 and -3, and here they're -3
43:14and -1. What's the idea here?
43:16These aren't the only other possible payoffs.
43:18It's just an idea. Suppose I get an A and my pair
43:23gets a C, then sure I get that initial payoff of 3,
43:28but unfortunately I can't sleep at night because I'm feeling so
43:32guilty. I have some kind of moral
43:34conscience and after I've subtracted off my guilt feelings
43:38I end up at -1, so think of this as guilt:
43:41some notion of morality. Conversely, if I chose a Beta
43:46and my pair chooses an Alpha, so I end up with a C and she
43:50ends up with an A, then you know I have a bad time
43:53explaining to my parents why I got a C in this class,
43:56and I have to say about how I'm going to be president anyway.
43:59But then, in addition, I feel indignation against this
44:02person. It isn't just that I got a C;
44:03I got a C because she made me get a C, so that moral
44:10indignation takes us down to -3. So again, I'm not claiming
44:16these are the only other possible payoffs,
44:18but just another possibility to look at.
44:21So suppose these were the payoffs in the game.
44:24Again, suspend disbelief a second and imagine that these
44:27actually are your payoffs, and let me ask you what you
44:29would have done in this case. So think about it a second.
44:33Write it down. Write down what you're going to
44:35do on the corner of your notepad.
44:36Just write down an Alpha or Beta: what you're going to do
44:38here. You're not all writing.
44:40The guy in the England shirt isn't writing.
44:41You've got to be writing if you are in an England shirt.
44:45Show it to your neighbor. Let's have a show of hands,
44:49again I want you to keep your hands up so that Jude can see it
44:52now. So how many of you chose Alpha
44:55in this case? Raise your hands.
44:57Come on, don't be shy. Raise your hands.
44:58How many chose Beta in this case?
45:01How many people abstained? Not allowed to abstain:
45:04let's try it again. Alpha in this case?
45:05No abstentions here. Beta in this case?
45:09So we're roughly splitting the room.
45:12Someone who chose Alpha? Again: raise the Alpha's again.
45:15Let me get this guy here. So why did you choose Alpha?
45:20Student: You would minimize your losses;
45:22you'd get 0 or -1 instead of -3 or 1.
45:26Professor Ben Polak: All right, so this gentleman is
45:27saying - Student: There's no dominant strategy so -
45:28Professor Ben Polak: Right,
45:29so this gentleman's saying, a good reason for choosing
45:33Alpha in this game is it's less risky.
45:35The worst case scenario is less bad, is a way of saying it.
45:39What about somebody who chose Beta?
45:40A lot of you chose Beta. Let's have a show of hands on
45:43the Beta's again. Let me see the Beta's again.
45:45So, raise your hands. Can we get the woman here?
45:48Can we ask her why she chose Beta?
45:51Student: Because if you choose Alpha,
45:53the best case scenario is you get 0,
45:55so that's - Professor Ben Polak: Okay good,
45:56that's a good counter argument. So the gentleman here was
45:58looking at the worst case scenario, and the woman here was
46:01looking at the best case scenario.
46:02And the best case scenario here looks like getting a 1 here.
46:07Now, let's ask a different question.
46:09Is one of the strategies dominated in this game?
46:14No, neither strategy is dominated.
46:15Let's just check. If my pair chooses Alpha,
46:18then my choosing Alpha yields 0, Beta -3: so Alpha would be
46:22better. But if my pair chooses Beta
46:25then Alpha yields -1, Beta yields 1:
46:28in this case Beta would be better.
46:30So Alpha in this case is better against Alpha,
46:33and Beta is better against Beta, but neither dominates each
46:37other. So here's a game where we just
46:40change the payoffs. We have the same basic
46:42structure, the same outcomes, but we imagine people cared
46:45about different things and we end up with a very different
46:47answer. In the first game,
46:49it was kind of clear that we should choose Alpha and here
46:52it's not at all clear what we can do--what we should do.
46:55In fact, this kind of game has a name and we'll revisit it
46:58later on in the semester. This kind of game is called a
47:04"coordination problem." We'll talk about coordination
47:09problems later on. The main lesson I want to get
47:12out of this for today, is a simpler lesson.
47:14It's the lesson that payoffs matter.
47:17We change the payoffs, we change what people cared
47:20about, and we get a very different game with a very
47:23different outcome. So the basic lesson is that
47:27payoffs matter, but let me say it a different
47:32way. So without giving away my age
47:34too much--I guess it will actually--when I was a kid
47:36growing up in England, there was this guy - there was
47:39a pop star--a slightly post-punk pop star called Joe Jackson,
47:43who none of you would have heard of, because you were all
47:45about ten years old, my fault.
47:46And Joe Jackson had this song which had the lyric,
47:50something like, you can't get what you want
47:53unless you know what you want.
47:56As a statement of logic, that's false.
48:00It could be that what you want just drops into your lap without
48:03you knowing about it. But as a statement of strategy,
48:05it's a pretty good idea. It's a good idea to try and
48:08figure out what your goals are--what you're trying to
48:11achieve--before you go ahead and analyze the game.
48:14So payoffs matter. Let's put it in his version.
48:21"You can't get what you want, till you know what you want."
48:39Be honest, how many of you have heard of Joe Jackson?
48:42That makes me feel old, oh man, okay.
48:47Goes down every year. So far we've looked at this
48:52game as played by people who are evil gits, and we've looked at
48:57this game as played by people who are indignant angels.
49:02But we can do something more interesting.
49:04We can imagine playing this game on a sort of mix and match.
49:08For example, imagine--this shouldn't be hard
49:11for most of you--imagine that you are an evil git,
49:15but you know that the person you're playing against is an
49:20indignant angel. So again, imagine that you know
49:24you're an evil git, but you know that the person
49:26you're playing against or with, is an indignant angel.
49:30What should you do in that case? What should we do?
49:36Who thinks you should choose Alpha in that case?
49:38Let's pan the room again if we can.
49:40Keep your hands up so that you can see.
49:44Who thinks you should choose Beta in that case?
49:47Who's abstaining here? Not allowed to abstain in this
49:50class: it's a complete no-no. Okay, we'll allow some
49:52abstention in the first day but not beyond today.
49:54Let's have a look. Let's analyze this combined
49:59game. So what does this game look
50:03like? It's an evil git versus an
50:07indignant angel and we can put the payoff matrix together by
50:16combining the matrices we had before.
50:22So in this case, this is me as always.
50:27This is my pair, the column player.
50:30My payoffs are going to be what? My payoffs are going to be
50:34evil-git payoffs, so they come from the matrix up
50:37there. So if someone will just help me
50:38reading it off there. That's a 0, a 3,a -1, and a 1.
50:47My opponent or my partner's payoffs come from the indignant
50:52angel matrix. So they come from here.
50:54There's a 0, a -3, a -1, and a 1.
51:01Everyone see how I constructed that?
51:02So just to remind you again, the first payoff is the row
51:05player's payoff, in this case the evil git.
51:08And the second payoff is the column player's payoff,
51:12in this case the indignant angel.
51:14Now we've set it up as a matrix, let's try again that
51:17question I asked before. Suppose you're the row player
51:20here. You're the evil git.
51:21Those are your payoffs. You're playing against an
51:25indignant angel, what would you do?
51:27So once again, no abstentions this time:
51:29who would choose Alpha? Let's have a show of hands
51:32again, keep your hands up a second.
51:34Who would choose Beta? Very few Beta's,
51:38but mostly Alpha's. Alpha, I think,
51:40is the right answer here but why?
51:42Why is Alpha the right answer here?
51:45Yeah, can we get this guy here? Student: It's the
51:47dominant strategy. Professor Ben Polak:
51:48Good. Actually nothing has changed
51:50from the game we started with. The fact that I changed the
51:52other guy's payoffs didn't matter here.
51:54Alpha was dominant before--it dominated Beta before--and it
51:58still dominates Beta. Let's just check.
52:01If my opponent chooses Alpha and I choose Alpha,
52:04I get 0; Beta, I get -1.
52:05So Alpha would be better. If my opponent chooses Beta and
52:09I choose Alpha, I get 3;
52:10Beta, I get 1. Once again Alpha is better.
52:13So as before, Alpha does better than Beta for
52:15me, regardless of what the other person does.
52:18Alpha dominates Beta. What was the first lesson of
52:24the class? Shout it out please.
52:27Right, so you should all have been choosing in this game,
52:31you all should have chosen Alpha.
52:34So the one person who didn't we'll let him off for today.
52:37So Alpha dominates Beta here. Let's flip things around.
52:50Suppose now--harder to imagine, but let's try it--suppose now
52:55that you are an indignant angel and you're playing against,
53:00and you know this, you're playing against an evil
53:06git. You're an indignant angel,
53:09so you have the payoffs that are still there and you're
53:11playing against an evil git, which is the payoffs we covered
53:14up but we'll reproduce them. Let's produce that matrix.
53:17By the way, if this is beginning to sound like a
53:19wrestling match, I don't mean it to.
53:22Let's try here: Alpha, Beta,
53:26Alpha, Beta, pair, me.
53:29So my payoffs this time, are the indignant angel
53:32payoffs. So mine are 0, -1, -3, and 1.
53:41And my opponent's payoffs are what would have been my payoffs
53:44before. They come from the other matrix.
53:46Let's just show you it. They come from this matrix.
53:48So they're going to be 0, -1,3, 1.
53:56I took the second payoff from that matrix and made it the
54:02second payoff in this matrix. Everyone see how I did that?
54:06Once again, the row player is the first payoff and the column
54:11player is the other payoff. What should you do in this case?
54:15You're the indignant angel. You're playing against this
54:18evil git. What should you do?
54:19Write down on your notepad what you should do.
54:21Show it to your neighbor so you can't cheat, or you can cheat
54:26but you'll be shamed in front of your neighbor.
54:30Raise your hands. Let Jude see it.
54:31Raise your hands and keep them up if you chose Alpha now.
54:37How about if you chose Beta now? So one or two Beta's,
54:41mostly Alpha's. Well let's see.
54:43Let's reason this through a second.
54:45Does my Alpha dominate my Beta? No, in fact,
54:50Alpha doesn't dominate Beta for me.
54:52It doesn't dominate Beta. If my pair chooses Alpha then
54:56Alpha gets me 0; Beta -3.
54:58So Alpha does better. But if my pair chooses Beta,
55:01then Alpha gets me -1; Beta gets me 1.
55:03In this case Beta is better. As we saw before,
55:06Alpha is better against Alpha. Beta is better against Beta.
55:09There's no dominance going on here.
55:12Nevertheless, at least 90% of you chose Alpha
55:15here, and that's the right answer.
55:17Why? Why should you choose Alpha
55:20here? Somebody …
55:22can we get the guy with the beard here?
55:25Wait for the mike, great. Student: We had
55:28acknowledged that Alpha is a dominant strategy for my
55:30opponent so we must choose based upon,
55:32or knowing that my partner is going to choose Alpha.
55:34Professor Ben Polak: Good, and your name is?
55:36Student: Henry. Professor Ben Polak:
55:37Henry. So Henry is saying sure I don't
55:39have a dominated strategy. My Alpha doesn't dominate my
55:44Beta. But look at my opponent.
55:46My opponent's Alpha dominates her Beta.
55:49If I choose Alpha and she chooses Alpha to get 0;
55:54Beta she gets -1. Alpha is better.
55:56If I choose Beta, if she chooses Alpha she gets
56:003; Beta 1.
56:01Again Alpha is better. For my opponent,
56:04Alpha dominates Beta. So by thinking about my
56:08opponent, by putting myself in my opponent's shoes,
56:11I realize that she has a dominant strategy,
56:15Alpha. She's going to choose Alpha and
56:18my best response against Alpha is to choose Alpha myself.
56:22So here, this time, my Alpha does not dominate Beta
56:32but my pair's choice of Alpha dominates her choice,
56:43her possible choice of Beta. So she will choose Alpha.
56:55And once I know that she's going to choose Alpha,
56:59it's clear that I should choose Alpha and get 0 rather than Beta
57:03and get -3. So I should choose Alpha also.
57:13Okay, so now we've seen four different combinations.
57:16We've seen a case where an evil git was playing an evil git;
57:19where an indignant angel was playing an indignant angel;
57:21and we've seen both the flips of those: the evil git versus
57:23the indignant angel; and the indignant angel against
57:25the evil git. Why are we doing this?
57:27Because there's an important lesson here.
57:29What's the lesson here? The lesson is--comes from this
57:32game--that a great way to analyze games,
57:35a great way to get used to the idea of strategic thinking,
57:39perhaps even the essence of strategic thinking,
57:42is the ability to put yourself in someone else's shoes,
57:46figure out what their payoffs are, and try and figure out what
57:51they're going to do. So the big lesson of this game
57:54is--I forgot what number we're up too--I guess this is Lesson 4
57:58I think. Lesson 4 is:
58:03put yourself in others' shoes and try to figure out what they
58:25will do. In a sense, this is the first
58:30difficult lesson of the class. It's easy to spot when a
58:33strategy is dominant, more or less.
58:35It's pretty easy to figure out, you have to know about your own
58:38payoffs. But the hard thing in life,
58:40is getting you to come out of your own selves a bit,
58:43realizing it's "not all about you."
58:45You've got to put yourself in other people's shoes to figure
58:48out what they care about and what they're going to try and
58:50do, so you can respond well to that.
58:54While we're here, let's just mention that things
58:57will get more complicated in a world where I don't actually
59:00know the payoffs of my opponent. It's much easier to figure out
59:04my own payoffs than to figure out my opponent's payoffs.
59:07I might not know whether I'm playing someone who's an evil
59:10git or an indignant angel. So I'm going to have to figure
59:12out what the odds are of that in doing this exercise.
59:15And we're going to come back to that idea too way at the end of
59:19the class, but that's getting a bit ahead of ourselves,
59:22but we'll get there. Now, it turns out that this
59:24game, this Prisoner's Dilemma, with the Alpha's and Beta's,
59:27or essentially the same game, has been played many,
59:30many, many times in experiments.
59:32So out there in the real world--I think we can do this
59:35here--out there in the real world when they do these
59:39experiments, they find out that roughly 70%
59:45of people choose Alpha and roughly 30% choose Beta.
59:54Roughly, almost a third choose Beta.
59:57What do we think is going on? That's a third of the people
1:00:01who seem to be choosing a dominated strategy …
1:00:04or is it? What's going on there?
1:00:06Why do you think 30% of people are choosing Beta?
1:00:13Anybody? Can we catch this guy here?
1:00:17Student: They might be motivated by the fact that every
1:00:21person who chooses Beta raises the average score.
1:00:24Professor Ben Polak: They could be moral people.
1:00:26So one possibility is: this 30% of people in the real
1:00:30world who choose Beta are just nice people.
1:00:32What else could it be? Yeah?
1:00:36Student: I know this might be changing the game a
1:00:38little bit, but if you ever expected to play the same game
1:00:40with the partner you have more [inaudible]
1:00:41Professor Ben Polak: All right,
1:00:42they could be thinking they're going to play again.
1:00:45Student: [inaudible] long run payoffs are greater if
1:00:47you choose Beta every time. Professor Ben Polak: So
1:00:49it could be that they think that this is actually--they haven't
1:00:51understood the experiment and they think this is a multi shot
1:00:52game, not a one shot game, good.
1:00:55What else could it be? What's the simplest explanation?
1:00:57What's the other obvious explanation?
1:01:00They could just be stupid, right?
1:01:01It could be., Are we allowed to say that in
1:01:03class? Let's be honest here,
1:01:05when we say experiments in the real world in Game Theory--or
1:01:08the ones you read about in The New York Times--the real world
1:01:11when it comes to experiments in Economics really means
1:01:14undergraduates at the University of Arizona.
1:01:17I mean, I'm not making it up. It just does.
1:01:20They all are. I don't know anything about
1:01:23… are any of you from Arizona, I don't know.
1:01:25I don't know whether the average undergrad at the
1:01:27University of Arizona just has a sunny personality or whether
1:01:30they "spent too long in the sun."
1:01:32I just don't know which it is, right?
1:01:36We can't really distinguish from this.
1:01:38How about at Yale. What's our numbers here.
1:01:41How about in this class? Do you want to mike your
1:01:46colleague here? So 238 at Yale--this is
1:01:52Yale--versus 36. So even at my level of
1:01:56arithmetic that's a lot less than 30%.
1:01:59That's more like less than 15%. It's about 15% I guess.
1:02:03So 236--I'm sorry 238--chose Alpha, and 36 chose Beta.
1:02:09Now there's one more lesson in this class and this is going to
1:02:11be it. This isn't the end of the class
1:02:13but one more lesson to take home.
1:02:15You guys are going to be playing games among each other
1:02:18today and until--whatever it is?--December 7,
1:02:21whatever is the end of term. Look around each other.
1:02:24You better get to know each other a bit.
1:02:26And what did we learn today about you guys?
1:02:31The lesson here, Lesson 5, is "Yale students are
1:02:39evil." Be aware of that when you're playing games.
1:02:48I want to play one more game today in the remaining minutes.
1:02:51It doesn't matter if we finish a little bit early,
1:02:52but I want to try to get this game at least started.
1:02:54So do you all have Game #2 in front of you?
1:02:58Just while you're reading that over, can I also make sure
1:03:00you've all got your legal forms and you're going to sign.
1:03:03Don't walk away with your legal forms, we need to get those
1:03:05collected in. So at the end of talking about
1:03:07this game, I'm going to collect in both the second game for the
1:03:11class and also the legal form. If you don't have a legal form,
1:03:15if you've lost it or something, it's online.
1:03:19Let's have a look at that second game.
1:03:20I'll read it out for you. Game 2: "pick a number."
1:03:28Everyone got this? Anyone not got this?
1:03:30Everyone got it? Good.
1:03:32"Without showing your neighbor what you're doing,
1:03:35put in the box below a whole number between 1 and a 100
1:03:39[whole number between 1 and 100--integer.]
1:03:42We will calculate the average number chosen in the class.
1:03:46The winner in this game is the person whose number is closest
1:03:50to two-thirds times the average in the class."
1:03:54[Again: the winner is the person whose number is closest
1:03:59to two-thirds times the average number in the class.]
1:04:03The winner will win $5 minus the difference in pennies
1:04:07between her choice and that two-thirds of the average."
1:04:12Just to make sure you've understood this,
1:04:16let me do an example on the board.
1:04:20I've got one more board; that's good.
1:04:23So imagine there were three people in the class,
1:04:29and imagine that they chose 25,5, and 60.
1:04:35So 25 plus 5 plus 60 is 90. People should feel free to
1:04:40correct my arithmetic because it's often wrong;
1:04:4290 right? Two-thirds of 90,
1:04:47whoops, what do I need, start again.
1:04:54I need to divide it by three to get the average.
1:04:56So the average is 30. So the total is 90,
1:05:03the average is 30, am I right so far?
1:05:06So two-thirds of the average is 20.
1:05:14I'm looking desperately at the T.A.
1:05:15Is that right? Okay, so the average is 30 and
1:05:18two-thirds of the average is 20. So who's the winner here,
1:05:22which number would have won here?
1:05:2425 would have won. 25 would have been the closest,
1:05:28and what would they have won? They would have won five bucks
1:05:34minus five cents for a total of four ninety-five.
1:05:40Now to make this interesting, let's play this for real.
1:05:44So this of course relies on me having brought some money and
1:05:48we'll have to do this without dislodging the microphone.
1:05:53So I'm going to see if I have… sorry about that.
1:05:55I'm going to see if I have enough money to do this in class
1:05:57for real. When we played this game in the
1:05:59old days, during the dot com boom with the MBA students,
1:06:03you had to put fifty dollars on the table to get them
1:06:06interested. Graduate students:
1:06:08five cents will do it. Okay, so this is a--there's
1:06:12some bloke with a beard on this one.
1:06:14Yeah this is Lincoln apparently. Who knew, Lincoln?
1:06:18Okay, so this is a five-dollar note and I'm going to put
1:06:21it--sorry about that again--I'm going to put it in an envelope.
1:06:25I'm not cheating anybody? No magic tricks here.
1:06:30And this is going to be the prize for this game and we
1:06:35better give this to someone we trust.
1:06:38It's the prize for 159.Who do you guys trust?
1:06:47The camera guy. Okay Jude: we know Jude's going
1:06:50to be there next week. I'm giving it to Jude.
1:06:52You can't see this on camera.--people at home--but I'm
1:06:54giving it to Jude okay. I'm going to put it here,
1:06:57and Jude has to show up next week with the prize.
1:07:01I thought we should give it to the guy at the back,
1:07:02who is the moral guy. Who is our moral guy at the
1:07:05back? Well never mind,
1:07:06we will give it to Jude. We know Jude's going to be here.
1:07:08All right, has everyone put a number down?
1:07:09Any questions? Just shout them out to me.
1:07:12Student: So given that we only have one five dollar
1:07:14bill does there have to be one unique winner,
1:07:15and if so, how is that determined if we have multiple
1:07:17people who are - Professor Ben Polak: That's a good
1:07:19question. If there's multiple winners,
1:07:21we'll divide it but we'll make sure everyone has a positive
1:07:23winning. Good question.
1:07:26Given the number of people in the room there may be multiple
1:07:28winners, I accept that possibility.
1:07:29Has everyone written down a number now?
1:07:31All right, so hand your numbers to the end of the row,
1:07:35but don't go yet. Hand it on to the end of the
1:07:37row. Before you go I want five
1:07:39things from you. I want to know the five lessons
1:07:44from this class. Tell me what you learnt?
1:07:47What were the five lessons? Without looking at your notes,
1:07:50what were the five lessons? Anybody, shout out one of the
1:07:52lessons, yes madam. Student: Don't play a
1:07:54strictly dominated strategy. Professor Ben Polak:
1:07:56Don't play a strictly dominated strategy, anything else?
1:07:58Yes sir. Student: Yale students
1:08:00are evil. Professor Ben Polak:
1:08:00Yale students are evil. Two lessons down, three to go.
1:08:03The guy over here. Student: Rational
1:08:05choices can lead to bad outcomes.
1:08:06Professor Ben Polak: Rational choices can lead to bad
1:08:09outcomes. We put it more graphically
1:08:11before but that's fine. Two more outcomes.
1:08:13Student: Put yourself in other people's shoes.
1:08:15Professor Ben Polak: Put yourself in other people's shoes
1:08:17and I'm missing one, I can't recall which one I'm
1:08:19missing now. Student: You can't get
1:08:20what you want so you - Professor Ben Polak: You
1:08:21can't get what you want. You could but it's a good idea
1:08:23to figure out what you want before you try and get what you
1:08:25want. Five things you learnt today,
1:08:28hand in your numbers and the legal forms and I'll see you on
1:08:32Monday.

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