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Hi. In this lecture, I'm gonna talk about what is by far the most famous game in

Â game theory. It's called the prisoner's dilemma. The prisoner's dilemma has been

Â written about literally tens of thousands of times. Far more than any other game and

Â it's a really simple game. There's only two players and two actions. So what we're

Â gonna do in this lecture is we're gonna talk about why the prisoner's dilemma is

Â so interesting, and we're gonna talk about some of the applications of the prisoner's

Â dilemma in a variety of different disciplines. Okay. So let's get started.

Â How does the prisoner's dilemma work? There's two players, player one and player

Â two. Player one will be. Role player, player two will be the column player. Each

Â player has two actions. They can cooperate, or they can defect. So here's

Â what makes the game so interesting. If both players co operate, if they are nice

Â to one another, each one gets a payoff of four, so player one gets a payoff of four

Â and player two gets a payoff of four. However if player two is being nice, if

Â player two is co operating and player one defects, then player one will get a payoff

Â of six. So it's entire one interested effect and since this game is symmetric,

Â if player one is co operating and player two defects, player two will also get a

Â payoff of six. Each one has an incentive to defect. Now if they?re both defecting

Â their both gonna get payoffs of two [laugh]. So here's the funny thing, it's

Â in their collective interest to cooperate. It's in their individual interest to

Â defect. But if they both defect their both worse off. So that's what makes the game

Â so interesting. By the way, if you're wondering why this is called prisoner's

Â dilemma, the original story behind the game goes as follows: two people are

Â caught, and the police are pretty sure that they've committed a crime, so they

Â put these two quote unquote prisoners in jail, They put them in separate rooms, and

Â they say to each one of them, look, you can rat out your friend, you can defect.

Â Or, the two of you could coope rate with one another. And not rat each other out.

Â Now if the two prisoners cooperate with each other and don't rat each other out

Â then they're going to get fairly mild prison sentences, but if they defect. And

Â they basically say, no, you're right, he, we did it, we did it. Then, each one would

Â get off, but if they both did that, and they both rat on each other, then they're

Â going to be worse off. So that's the original story behind the game. But we're

Â gonna see that there's far broader applications than sort of little vignettes

Â about prisoners going to jail. This game has lots and lots of applications. But

Â before we get into it, let's talk about, a little bit about what is a prisoner's

Â dilemma and what's not a prisoner's dilemma. So here's a game that sometimes

Â you'll see written down as a prisoner's dilemma but it's not. Here again, if they

Â both cooperate, they get four. If they both defect, they get two. But now if

Â player 2's cooperating and player one defects, player one gets a payoff of nine.

Â So nine is a huge payoff. And so if you look at this game, you realize that 4-4,

Â although it's a good payoff, is no longer the best payoff if this game is played

Â many times. Because if we're playing the prisoner's dilemma several times, what

Â can. After years, the two players can alternate. They can go nine, zero and

Â zero, nine and their average payoff By alternating. You'd be four and a half

Â which is bigger than four. So this game, which people sometimes put down as the

Â prisoner's dilemma game, actually isn't. It's a game I like to call weak

Â alternation; where you've got an incentive to alternate as opposed to cooperate. So

Â in the prisoner's dilemma, it's gotta be the case that you're better off playing

Â cooperate, cooperate. So when people write down formal definitions of the prisoner's

Â dilemma, they don't use numbers like four, two and six. Instead they write down

Â things like T, F and R. So here's the idea. For there to be a prisoner's

Â dilemma, T is gonna be bigger than R because that means you're better off

Â cooperating. Been defecting. It's also the case that F Has to be bigger than T,

Â because that means that player one would rather defect if player two is

Â cooperating. And player two would rather defect if player one is cooperating. And

Â then the third thing we need is that two T. Has got to be bigger than F, because

Â we've got to make sure that you're not better off alternating than playing

Â cooperation. So this is formally how we write down a class of games that belong to

Â what we call the prisoner's dilemma. Of course we're assuming here that T and R,

Â of course, are bigger than zero. Okay, so that's it, that's all there is to the

Â prisoner's dilemma. Why is it so interesting? Why all this focus on the

Â game? Well again, let's go back to the two things I talked about before. What's the

Â efficient, outcome, what's the thing you'd really want to get? You'd like to get C-C,

Â you'd like to be the case that both people are getting four. But supposing they had a

Â weaker notion of efficiencies. Cause here, by picking 4-4, that's the one that sort

Â of both get the same payoff, and it's got the highest total payoff. You can think of

Â another notion of Efficiency, which is called pareto efficiency. Now path is

Â pareto efficient to a group of people if there's no way to make everybody better

Â off. So there's no way in which you can make every single person better off. Well

Â that's clearly true of the case four, four. There's no way to make everyone

Â better off. But it's also true of zero six and six zero. Let's see why. Suppose we're

Â sitting at zero six, is there any way to make everyone better off? No, Because if

Â we go here then player two is worse off. If we go down here player two is worse

Â off. If we go here player two is worse off. And if we go here player two is worse

Â off. So there's no way to do, make everyone better Than getting 0-6. Player

Â 2's always gonna suffer. For the same reason 6-0 is also Pareto efficient.

Â There's no other payoff that we can get that makes player one better off, 'cause

Â that's player 1's highest payoff. In f act, the only thing in this game that

Â isn't Pareto efficient is 2-2. And the reason 2-2 isn't Pareto efficient is

Â 'cause we can make every better, everyone better off by going to 4-4. So what we get

Â in this game is there's only one outcome that's really bad if we use Pareto

Â efficiency as our criterion. And that outcome is 2-2. So the only thing that

Â isn't a good outcome in this game is 2-2. But, if we think of this in terms of game

Â theory, there's this notion of Nash equilibrium. And Nash equilibrium, it

Â seems that people optimize. Well let's look at the strategies that people should

Â follow. If I'm player one, and player two right here is cooperating, then I should

Â defect because six is better than four. But if player two is defecting, I should

Â also defect because two is bigger than zero. Now the same thing's two by two. If

Â player 1's cooperating Player two should defect, 'cause six is bigger than four.

Â And if player one is defecting, player two should defect, 'cause two is bigger than

Â zero. So the Nash Equilibrium here is 2-2. Well, this is why the game is so

Â interesting. There's three efficient outcomes, in some sense 4-4, 0-6, and 6-0.

Â Any one of these things you could argue, on moral grounds, is sort of an okay or

Â efficient outcome. Because there's no way to make everyone better off. But the only

Â equilibrium outcome here is two; two is the one inefficient thing. So what you

Â have is incentives don't line up with what we wanna have occur socially, so there's

Â this disconnect. And it's that disconnect that is so interesting to people when they

Â study the prisoner's dilemma. 'Cause what we wanna do is we'd like to have a way to

Â have the outcomes that we get in a situation align with our social

Â preferences. And what happens in the prisoner's dilemma is our individual

Â preferences point in one direction, which is toward defect. And our social

Â preferences head in another direction, our collective preferences, which is to

Â cooperate. It is that tension that creates so much interest. Now that's not gonna be

Â true of most games. Right? So here's another game called the self interest

Â game. Where again if I look at player one and player two, they've each got two

Â strategies, A and B. And what you see is that player one would rather play B if

Â player 2's playing A, And if player 2's playing B. We would also like to play

Â deep. For the same reason if player one is playing A you get to player two would

Â rather play B. Cuz six is bigger than four. And if player one is playing B.

Â Player two would also like to play B. So what we get is the equilibrium in this

Â game Is 7-7. So if people are strategic, what you're gonna get is 7-7. But that's

Â also the only pareto efficient outcome. So here what we get is the pareto efficiency

Â lines up with incentives. So the self-interest game, nobody writes many

Â papers about this, [laugh], because it's obvious what's gonna happen. You're gonna

Â get 7-7, and that's what we'd like to get. So therefore, there's no dilemma. There's

Â no problem. But the prisoner's dilemma has a problem because what we are going to get

Â is 2-2 and what we want is 4-4. So the question is how do we get it. Before I go

Â on to talking about how we get corporations [inaudible] let?s talk a

Â little bit about why it has been of so much interest. The reason is it sort of

Â applies to a lot of settings. Here's one, let's think about arms control. You can

Â think about corporations, spending money on education and you can think about

Â defections spending money on bombs. So now you got two countries, Country One and

Â Country Two. Both countries would prefer if they were both spending their money on

Â education. They can't help themselves and they spend money on bombs and everyone

Â else is worse off. Look at price competition between two firms. So you got

Â two firms competing. Maybe two ice cream stores right next to each other.

Â Cooperation would be, let's keep prices high, and the firms make money. Defection

Â would mean that they lower their prices to get more customers. Well, if they both

Â lower their prices, they're both worse off. So what they'd prefer to d o is have

Â high prices, and get higher payoffs. But it's in their individual interest to have

Â lower prices, and so they end up being worse off. Now in this case, the

Â prisoner's almost interesting because even though the firms are worse off, the

Â consumers are better off. So don't really care too much about this type of

Â prisoner's dilemma, at least not as much as we care about the situation of taking

Â money that could go to education and spending it on bombs. Similar logic holds

Â for technological adoption. So let's think of two banks. And the banks can decide

Â either not to buy ATM machines or to buy ATM machines. If they don't buy ATM

Â machines Both make profits of, let's say, four. However, if one of'em buys an A-,

Â buys ATM machines, and puts them up all over town, everyone will go to that bank.

Â And so if this bank defects, bank one defects, they're gonna get a higher payoff

Â of six. But if bank two comes in and puts in ATM machines, what's happened? Well

Â now, both of them have probably the same customers they had to start out with, but

Â they've spent all this money on ATM machines. So they're actually worse off.

Â In fact, it could even be worse than that. Because [inaudible] maybe before, part of

Â the reason they made such profits is because they got geographic grants. People

Â who lived around the bank shopped at that bank. Now that there's ATM machines

Â anywhere, people can shop whatever bank they want. And that's created more price

Â competition, like our previous prisoner's dilemma game. And so the banks end up not

Â doing as well. So again, they prefer not to buy the ATM machines. They can't help

Â themselves. They're both worse off. But again, in this case, like the price

Â deter-, the price competition case, we end up with the consumers being better off.

Â Let's look at political campaigns now. Suppose you got two candidates running for

Â office and it's a pretty even race. They could both run purely positive ads. And

Â what happened is they get some vote total but they also had some really shining

Â reputations. But now one of th ''em thinks, I'm gonna go negative. I'm gonna

Â bring up the fact that this one person went on a whole bunch of junkets paid for

Â by private industry. And by doing that I'm gonna win the election. But now the other

Â person goes negative as well and your back to having a 50, 50 chance of winning the

Â election. And your tarnished, your reputations tarnished. So, your payoff is

Â lower. So you'd both be better off if you only ran positive ads but you can't help

Â yourself and so you run the negative ads. It's a prisoner's dilemma, Food sharing.

Â Let's think of the simple case where there's two of us, and we can decide

Â either, share food or not share food. So if we both share food, then we're gonna

Â get a payoff A four. But if I don't share with you and you share with me, I'm gonna

Â get a payoff of six, so I'm much better off. Now if neither one of us shares,

Â we're worse off because the thing is, by me not sharing with you I don't get to get

Â your food. Now why would your food be different than my food? Well, it's two

Â reasons. One is, it could be that you actually, you have apples and I have pears

Â so we can get both types of food and be better off. And the other thing it could

Â be that maybe some years I do well and you do poorly, and some years you do well and

Â I do poorly, and so by sharing with one another, we spread the risk. Either one of

Â those logics applies; we're better off collectively sharing. However, we're

Â individually better off if we don't share and the other person shares with us. So

Â again, it's a straight prisoner's dilemma. And then finally, Adonis treadmills, So

Â let's suppose, you're thinking about something like getting a fancy watch. Well

Â it could be that we both just wear nice digital watches and they keep time and

Â everything's fine. But then, I decide, you know what? I'm gonna go buy this fancy,

Â handmade watch for $5,000. I'm gonna take all of my savings and go buy a handmade

Â watch. No why, why would I benefit from that? I'm gonna benefit from that because

Â people are gonna look at me and say, wow. Look how succ essful Scott is. He's got

Â that fancy watch. And you're gonna feel badly, cuz you're gonna feel like, wow,

Â you know, I don't look as cool as Scott looks cuz I have this cheap Plastic

Â digital watch. So then what happens is, you go buy A fancy handmade watch. Well,

Â we're both wearing fancy handmade watches, and neither one of us looks any cooler

Â than the other, but we've spent all the money that we could have used to send our

Â kids to college, let's say on watches. So, we're both worse off Classic prisoner's

Â dilemma. Okay, so in this lecture, what have we seen? We've seen the prisoner's

Â dilemma's a really simple game. Two players, two actions, We've seen it

Â applies to a whole bunch of settings, from arms control, to buying watches, to

Â sharing food, to price competition, to technological adoption, tons of

Â applications. And we've seen the reason it's so interesting is because what people

Â are gonna tend to do Is give us an outcome that isn't efficient. What we'd like to do

Â is typically have situations in the real world where the outcomes we get are the

Â good outcomes but when we have a prisoner's dilemma, the outcome we get may

Â be the bad outcome. What we want to do next, is see how do we get cooperation,

Â how do we get that four, four. We're going to see there's a variety of ways in which

Â that can be achieved. Alright, thank you.

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