Philosophy and the Science of Human Nature

PHIL 181 - Lecture 20 - The Prisoner's Dilemma

Chapter 1. The Prisoner’s Dilemma [00:00:39]

Professor Tamar Gendler: All right. So, what I want to talk about today in lecture is a game theoretic notion known as The Prisoners' Dilemma, which can be used to characterize a structure that is brought out both in Book Two of Plato's Republic and in chapter 13 of Hobbes' Leviathan.

And the purpose of introducing you to this way of thinking about questions is exactly what we have been doing all semester long. It's taking a traditional set of philosophical issues and asking how it is that another discipline's methodology can shed light on those questions in a complementary way.

So you'll recall at the beginning of the last lecture that I started off with a quote from the beginning of Book Two of Plato's Republic when Glaucon is answering Socrates' challenge to articulate the nature and origins of justice--the nature and origins of, roughly speaking, pro-social behavior.

And I pointed out that the claim that Glaucon makes there takes the form as follows. “They say that to do [justice] injustice is naturally good, to suffer injustice is bad, but that the badness of suffering so far exceeds the goodness of doing it that those who have done and suffered injustice and taken both but lack the power to do it and avoid suffering, decide that it's profitable to come to an agreement with each other neither to do injustice nor suffer it.”

And we illustrated that with the example of the two shepherds, one of whom steals another's horses and gains a certain amount of pleasure from it, but not as much as the displeasure that the stolen fellow receives likewise when the second steals the first. So both of them end up in a situation with less utility than they would have if they were cooperating and they come together and form some sort of pact.

Glaucon continues with the passage that I also read you last class. He says, "Justice is intermediate between the best and the worst. The best is to do injustice without paying the penalty. The worst is to suffer it without being able to take revenge. Justice is a mean between these two extremes."

But I didn't read you the sentence that follows that, which is one on which we'll be focusing in today's lecture. Because Glaucon continues by pointing out that on his view, and it will turn out, if you were thinking of justice as this kind of coordination, on anybody's view mathematically--can I ask one of the TFs to fix the door so that it doesn't slam as people walk in? What he says is, “People value it not because it is a good, but because they are too weak to do injustice with impunity.” Someone who has the power to harm another without being harmed himself, someone who has the power to do this, however, wouldn't make an agreement with anyone not to do injustice in order not to suffer it. “For him, that would be madness.”

So Glaucon has given us an argument that we're going to see again in a minute in Hobbes that takes the following form. It is rational when you think there is no choice but to cooperate, to cooperate. But if you think you can get away with having the other person cooperate while you act in a non-cooperative fashion, it would be insane for you to cooperate. It would be madness.

Hobbes makes exactly the same point in Chapter 13 of Leviathan. You'll remember that he articulates there the first two laws of nature. Laws of nature, remember, are norms to which rational beings qua rational beings are bound, because they recognize that in following those norms they increase the likelihood of preservation and flourishing in their own lives.

So the first law of nature is a two-part law. It says seek peace if there's a chance of obtaining peace, and if there is not, engage in war. The second law of nature, as you'll recall, also articulates a conditional commitment to giving up a certain sort of freedom. The second law of nature tells you to be willing to lay down your rights to the extent that others are willing to do the same, and to content yourself with as much liberty against others as they have against you.

So again, as in the first law of nature, the giving up of rights is conditional on others giving up rights as well. Like Glaucon, Hobbes gives voice to the concern that this may not be feasible. He writes, “If other men will not lay down their right as well as he, there is no reason for anyone to divest himself of his. For to do that would be to expose himself to prey which no man is bound to, rather than to dispose himself to peace.”

We're going to be using the clickers after the next slide, so if you get your clickers out you'll be prepared for that. Now, I know that some of you in this class are economics majors and some of you in this class have taken game theory. And to those of you, I apologize in the way that I apologize to the philosophy majors for introducing you at a basic level to Plato's Republic. But this is a resource that all of us need to understand the class, and I promise that there are some actual games that we'll be playing in a few minutes.

So the Prisoners' Dilemma is a way of representing in graphic form the structure to which both Glaucon and Hobbes adverted. And it involves representing a pair of choices by a pair of people on a two-by-two matrix. So there is on the one hand an individual, A, who faces two possibilities for action. The first is that she can behave in a peaceful way, lay down her rights to attack her enemy and thereby give up a certain kind of freedom. Or she can reserve for herself the right to war and thereby produce in her challenger a feeling of threat throughout.

Her counterpart, B, faces exactly the same pair of choices. He can behave peacefully and lay down his right to attack, or he can reserve the pleasures of war for moments when he feels himself, either preemptively or retaliatorily, to need to engage in threatening behavior. Now what's important to notice about the prisoners'--sorry. So that gives us four possibilities. Either A and B can both behave in peaceful fashion. That is, they satisfy the initial clause of Hobbes' first law of nature. They do the handshake of Glaucon's challenge; they each give up to the same amount what Hobbes talks about in the second law of nature. Or, they can both be in a state of war with one another. This is what Glaucon thinks will naturally arise and what Hobbes thinks is the case in the state of nature. Or it can be the case that A, the letter on the left refers to A, behaves peacefully, whereas B behaves in a war-like fashion. Or it can be the case that A behaves in a war-like fashion, whereas B behaves in a peace-like fashion.

Now what's important to notice about the structure of The Prisoners' Dilemma, is that A has control over which row obtains. A can determine whether we're in this row or this row. But A has no control over which column obtains. B, by contrast, has control over which column obtains, and no control over which row obtains. B can determine whether we're on the left hand column or the right hand column, but B can't determine through his direct behavior whether we're in the top row or the bottom row.

Now, I want to just start by making sure that everybody has understood the structure of this problem, because as I said I'm about to put some real money on the line for you, and I want to make sure that when you make the decision, you make it understanding the structure of the case.

So let me start by telling you what A's preference structure is with regard to outcomes, and then ask you with your clickers to tell me which choice is rational for A to make. So as we know from Glaucon, everybody's first choice is to reserve for themselves all the rights, but to have their opponent lay down his rights. So A's first choice is that A is war-like and B is peace-like. Everybody's fourth choice, as Glaucon points out, is to be stuck having laid down their arms when their enemy hasn't done so. To be cooperating when their enemy is failing to cooperate. So that's A's fourth choice.

But as Glaucon and Hobbes both point out, between the choice of peace-peace and war-war, that is, a state of nature or a state of society where there's been a mutual laying down of rights, it is everybody's second choice, in particular A's second choice, to be in a peaceful state and A's third choice to be in a state of total war.

So the question that I want you to answer--so the choice that A makes is which row we're in. A can put herself in a row where she's either going to get her second choice or her fourth choice. Or she can put herself in a row where she's going to get either her first choice or her third choice. That's the decision A has to make. Second or fourth choice, versus first or third choice. That's it.

So, question, if you'll take out your clickers, is this. Which choice, given this matrix, is it rational for A to make? Is it rational for A to choose row one, where she will get either her second or fourth choice, or is it rational for A to choose row two, where she'll get her first or third choice?

OK. So. The 4% of you who want to punish the guy who didn't do things that are wrong, to cut up the guy who showed up naively at the hospital, and to choose the dominated choice in a prisoners' dilemma matrix are here with us always. Those of you reading psychology articles who wonder why it is that in doing statistical analysis one needs to leave room for experimental error, can see over and over in our classroom environment why that is so.

But 96% of the answers brought out what is inherently the structure of this situation, namely, that given a choice between peace, where A will get her second or fourth choice, and war, will she get her first or third, the obvious thing for A to do is to choose the lower row. So now we have A's decision made. What is rational for A to do is to choose the lower row.

The situation for B is of course exactly symmetric. B gets to choose the column, so B can choose--B's first choice would be that A is peaceful while B is war-like, B's fourth choice is that A is war-like, while he's peace-like. B's second choice is peace-peace and B's third choice is war-war.

So just to check again and let's see if I can get rid of that residual 4%, let's try again. What is the rational choice for B to make in this situation? If you do a good job on this, we'll go to the real money one. What is the rational choice for B to make in this situation, given that peace will give him his second or fourth choice and war will give him his first or third? So let's see how the numbers come out this time for us. Three, two, one second, and... [laughter]

Professor Tamar Gendler: Ha, ha, ha. All right. Excellent. So there we go. Ninety-two percent of you on eternity on the internet have given a rational answer, and 8% of you forever, anonymously, will be known to have put yourself in situation one. So the structure of The Prisoners' Dilemma with regard to B is also that the column that is rejected is the peaceful column.

So what we have is a situation where A determines the row, sorry, where B determines the column, and chooses the war-like column. A determines the row and chooses the war-like row. And the result of this is that it is a stable situation in dilemmas of this kind that everybody ends up with their third choice.

Now, the structure that we've just described in the context of the Glaucon-Hobbes style social contract question is of course a structure that emerges over and over again. Any choice situation where the person choosing the column has an array like this, and the person choosing the row has an array like this. That is, any situation where there is asymmetric first and fourth choices and symmetric second and third choices, will end up stably putting people in a situation where they both end up with their third choice.

So, for example, if we put people--we're police officers and we put criminals in a dilemma, this is why it's called The Prisoners' Dilemma--where we incentivize unilateral confession over staying silent, it will turn out that both prisoners will be motivated to confess, ending up with their third choice rather than what would have been their second, both staying silent.

If we are in a nuclear arms race with another country where mutual disarmament would leave both countries with a peace dividend, it will nonetheless be the case that the fear of the other party defecting and the fear of perhaps ending up in one of these cells, will push both parties to the third choice. Third choice.

If we are in the situation described at the beginning of today's reading, Hume's story of two individuals, both of whom would benefit if they put in the effort to drain the swamp outside of their field, neither of whom wants to be the only one to do it, you will get a non-cooperative situation.

And you face analogous situations with any sort of cooperative scenario where multiple people cooperating would produce an outcome that was beneficial for the group as a whole, but no individual wants to be the one who takes on an undue burden.

So vaccination is another example of a prisoners' dilemma. There's a certain low risk associated with vaccinating your child or yourself against a disease. There's a very, very low risk that the child will get very ill and a somewhat moderate risk that the child will have slight illness. On the other hand, if nobody engaged in vaccination, we would be much worse off. And, in fact, the motivation not to vaccinate would dissipate.

So more generally, prisoners' dilemmas arise when the cooperative situation is dominated by the defect situation. And the puzzle that we will talk about after we run through a few more examples is how, if at all, it's possible to move from this cell to this cell. So as I pointed out, prisoners' dilemmas arise in asymmetric cases where one-sided cooperation is the most costly option, where one-sided defection is the most beneficial option, where two-sided defection is somewhat costly, and where two-sided defection [correction: cooperation] is somewhat beneficial.

Chapter 2. The Classroom Dilemma [00:20:11]

Now, how are we going to do that in this class? Here's what I came up with. This is the classroom dilemma, and it's for real. It's for real. The money's right here and I have a list of the names of the students who are actually going to get money from this for each dilemma that we play. We're playing three right now. One of you, and I'll tell you afterwards, will actually get one of the following payoffs.

If you choose one, and the majority of the class chooses one, you will get $15. If you choose one, and the majority of the class chooses one, you will get $15. Here's a twenty right here, and I will make change for you. If you choose two, and the majority of the class chooses one, you will get $50. Fifty dollars. I'm betting on game theory here. If you choose one and the majority of the class chooses two--I wanted to put in a penalty here but I couldn't ask you for money. So you'll just get nothing. And if you choose two and the majority of the class chooses two, you will get $5.

Now, just to point out that I am good on my word, Sarah Cox, are you here today? Sarah Cox. Sarah Cox, did you get $5 from me on March--I'm sorry, on February 15? Yeah. Sarah Cox did get $5. And looking back over my notes made me realize that I never selected somebody for the second prize, and March 22 and 24 were last week, so Tara Abraham, are you here? Wow. Tara Abraham, you will get either, you will actually get $6, because I'm just going to assume that you were in the 97%. So come up after class and get your money.

OK. So I want to tell you that I'm serious, and here's the classroom dilemma. Here it is. If you choose one, you will get either $15 or zero dollars, depending on what the majority of the class does. If you choose two--swear, I'm totally serious--you will get either $50 or $5, depending on what the rest of the class does. I mean it. Start clicking. Only eight of you? Nobody wants the money? I'm going to start the timer. Don't miss your chance. This is real money. There is a list of names right here, for real. Those two people that I called are really here. These are not plants.

If you're not here somebody else will get the money. So bid away. You have 10, 9, 8, let's see whether game theory is on my side. All right, let's see what we got. OK. The majority of the class chose two, so there I am. And the individual selected is Charles Holmes. Charles Holmes, are you here? Charles Holmes is not getting what Charles Holmes might have gotten, which is either zero or $5--well, Charles Holmes is getting zero dollars, but not as a result of this. Sello Lekalakala, are you here? Sello Lekalakala Sello Lekalakala you--did you give an answer, Sello, of one or two? You gave an answer of two. Sello, after class, you may come up and get $5.

Let's try it again. Let's see whether I am going to have to pay my $50. OK? I was betting that I would have to give $5, and I did. Notice, you guys, you ended up in the bottom right hand corner of the prisoners' dilemma. OK? Let's try it again. Same game. Trying it again. I'm really risking, right? Go ahead. Do what you can. Try to get your $50. Give it your best shot. All right. 49 of you. Let me start the timer, and let's see how the numbers come out. Let's see in our 4, 3, 2, 1 second live for television audiences, 68 and 32. OK, so once again the majority has put us in two. So let's see whether the victor, what the victor is going to get. Either $50 or $5. Sorry, either zero or $5. The winner this time is Helen Wang. Helen Wang, are you going to get zero, or $5? Are you here, Helen? OK. Helen, did you give--are you getting zero dollars or $5? You're getting $5. Excellent.

All right. I'm out another $5. Let's try it one more time. Game theory on my side. Guys, you're in the bottom right hand corner. What's up? This is the prisoners' dilemma for you. Let's try it one more time. Which do you choose? Same bet all over again. OK? I have all the money right here. I stole it actually from my son's Bar Mitzvah folder. I don't have cash at home but he had a lot. All right. But I will fortunately be able to pay him back most of it, so he'll be grateful. OK. So let's see how our numbers are going. 49  of you up there again. Ten, nine, eight, seven, six, five, four, three, two, one. Let's see whether I'm going to lose some money. Fifty-four percent. You're getting closer. Ah ha. I put it up three times, thinking very, very hard that I didn't want to put it up a fourth. OK. So the winner this time, Jared Jones. Jared Jones, are you here? Jared Jones, OK. Jared, do you get zero dollars or $5? You picked two. So once again $5, and we are in the bottom right hand corner of the prisoners' dilemma.

OK, dudes, you missed out on the peace dividend, right? You would have been better off if somehow we could have ended up in the fifteen-fifteen cell. And the cooperation dividend, which was unavailable to you because of course this is a big room and you're seated in rows and you couldn't collude and there were no enforcement mechanisms. The cooperation dividend was unavailable to you.

What's the cooperation dividend look like? Well, it looks like this. Here are our two shepherds in the state of nature and each of them grows a garden. But because it's the state of nature, the green guy goes over to the red guy's garden and steals a tomato, and the red guy, angry at the green guy, goes over to the green guy's garden and smashes it up with his pitchfork. So the green guy says, I don't want the red guy smashing up my garden with his pitchfork. I'm going to put a fence around my garden, and he uses his effort to do that. And the red guy says, I don't want the green guy stealing my tomatoes, and he puts a fence around his garden.

If, however, they had somehow been able to cooperate, to make some sort of agreement whereby they would keep their hands off the other fellow's garden, instead of putting that effort into building the fences, they could have put their effort into what Hobbes calls the features of commodious living.

So the green fellow could've had a beautiful flower garden that attracts hummingbirds, and the red fellow could have developed a device that allows him to predict the motion of the planets.

When we don't have to expend energy on things like protecting our property, we have extra energy left over for things like commodious living. And just to remind you where that fits in the context of things, this is Hobbes' explanation for why it is rational for us to engage in a social contract.

Chapter 3. The Problem of the Commons [00:28:59]

What I want to do now is to introduce you to a second notion closely related to that of The Prisoners' Dilemma. Namely, The Problem of the Commons. And I'll give you three examples of that, and then we'll get to play one more game. And there's real money on the line there, so let me say I have a lot left over from the last round.

So here's The Problem of the Commons. Tragedy of the Commons. So suppose you live around a beautiful green area and you and your fellow shepherds each have a cow. So you put your cow out on the pasture to graze, and everything's going fine. Now there's a nice big pasture there, and in fact you would be better off if you had not one but two cows.

So you and each of your fellow shepherds gets a second cow, and puts it out in the pasture. But of course if two cows were good, three cows are better. So you and each of your fellow shepherds puts your extra cow out, and now you have three cows apiece. Three cows great, four cows, super duper. Each of you gets a fourth cow, puts it out to pasture. And the result, if the clicker will work, the result is that there is no more space left to graze. The pasture gets destroyed. So scarce resources become depleted through The Tragedy of the Commons.

Likewise, it's now the industrial revolution. We've made it past our shepherd days. You and your fellow industrialists each create one polluting plant, and here it is. Putting out a little bit of pollution. One polluting plant good, two polluting plants better, so out you go, and there's the profit. No idea why these are going non-cooperatively. There we go. You got your third plant super fast on account of the clicker. And out comes the fourth plant for each of you. Result, the entire environment is polluted. Each of you did the thing that was rational, but the coordinated effect of your actions gave you a wildly sub-optimal result, an environment full of pollution.

Notice that we can think of everybody in this class' favorite problem, the problem of procrastination, in light of The Tragedy of the Commons. Suppose this is a representation of the hours in your day. And this is your 9 a. m. self, and this is your noon self, and this is your 6 p.m. self, and this is your 10 p.m. self. Now, your 9 a.m. self and your noon self and your 6 p.m. self, and your evening self, all want to play a round of Angry Birds. But, you know what? One round good, two rounds better. Two rounds, good, three rounds great. Three rounds great, four rounds super, and all of a sudden you've spent your day playing Angry Birds.

So the structure that The Tragedy of the Commons confronts us with is not just one of depletion of resources. It's not just one of pollution of the environment and other sorts of degradation that result from actions that are individually non-problematic, but as an aggregate, lead to bad outcomes. It's also a way of thinking about one of the questions we've asked ourselves over and over in this course. Which is, how do we structure our lives in such a way that our long-term goals are the ones we achieve? And when I say I'm not kidding that the trope of the Republic, that the individual and society mirror one another in important ways, here's another place that I'm not kidding.

So let's play our own Tragedy of the Commons game. So here's how our Tragedy of the Commons game is going to go. OK. So the deal is this. Each of you can decide whether in this game, if you are the name called, and I have more names on my list, if you are the name called, whether you will take a reward of $1. If so, push one. Whether you will take a reward of $2, in which case, push two. Or whether you will take--I’m sorry, of $10, push two. Or whether you will take a reward if called, of $50. Fifty dollars.

There's a name on this list. There's roughly a hundred clickers, you have a one in 100 chance of $50 if you choose three. But here's the deal. If the total requested is less than $150, I'll reward the winning student with the amount that he or she has requested. But if the total requested, and I will say, I thought there would be more clickers than there are, this is a riskier game than I meant myself to be playing, but we will see. If the total requested is more than $150, Tragedy of the Commons, bank goes bust, too many requests, no reward. OK?

So, the game is there, 22, 23, 24--I'm going to hold off. I want a lot of responses to this game. Let's see how these numbers come in. All right, I am going to play fair. I'm going to start count down now. Ten, nine, eight, seven, six, five, four, three, two, one. You only came in at 85 responses? I may have to do some math. No, I don't have to do some math. Busted. You guys bankrupted the bank. There's no way, right? I mean, at 30 times 10, you're way over the $150. Greedy, greedy, greedy. Who didn't get their dollar? Kyle Cooper, I'm sorry. You would've gotten some money and you got nothing. All right. Now, that's an interesting psychological question, why it's worse to have gotten nothing that way than the way that all the rest of you got nothing? OK.

So, what's going on in The Tragedy of the Commons is what you see here. That is, each of you did what was individually rational, I mean, 18% percent of you went for the big money. But 38% of you went for $10. Only 45% of the students chose the option that was possible for everybody to take. You violated the categorical imperative.

All right. Well, that's life. But the question is, now that we've presented ourselves with these two versions of the puzzle, The Prisoners' Dilemma on the one hand and The Tragedy of the Commons on the other, what kind of strategies there are for escape.

Chapter 4. Strategies for Escaping the Problems [00:36:39]

And in the last 10 minutes of lecture, I just want to talk through at a very general level what kinds of strategies are available. So remember, the issue is this. Three out of three times, you all ended up in the bottom right hand corner of The Prisoners' Dilemma. You ended up with your third choice rather than what could also potentially have been a stable outcome, your second. And in The Tragedy of the Commons, you all, as a result of your expression of rational self-interest, ended up in a situation where, as an aggregate, you were worse off.

So what do we need to do to escape this situation? We need somehow to structure the decision situation so that we either decrease the relative utility of the sub-optimal behavior, or increase the relative utility of the optimal behavior. That is, somehow we want to make it the case that B isn't moving us over to the right, and that A isn't moving us down to the bottom. That's the only way for us to get out of this situation.

So we have various mechanisms that are available to us for doing this. We can introduce some sort of penalty or reward for the asymmetric cells in a way that will either make the one less appealing, or the four less repulsive. So that the siren call of the first choice doesn't beckon B in the same way to defect, and the fear of the fourth choice doesn't beckon A to defect. The result of having done this will be to create the potential for some sort of stable, sustainable equilibrium at the preferred cell. At our two-two, rather than our three-three.

So what sort of mechanisms are available in this context? Well, the first place we might look is to external penalties and external rewards. So one thing that we can do is simply to incentivize the cooperative behavior. We can do it with material incentives, like increased money or goods, things that are valuable. We can do it with social incentives. We can have status markers associated with cooperation. We can bring reputation costs into play. And when we play prisoners' dilemma games in sections next week, you'll have an opportunity to try out all of these things.

Or we can induce certain kinds of personal incentives. We can increase your freedoms or your privileges as a result of your having cooperated. And with respect to each of these kinds of incentives, there are counterparts which are penalties. So, there can be material penalties associated with non-cooperation. We can decrease your amount of money. We can take away some of your goods. There can be social penalties associated with non-cooperation. You could face a decrease in status or a decrease in reputation. Or, there could be personal costs associated with non-cooperation. Decreases in freedom, or decreases in your privileges.

So these are the sorts of penalties and rewards that can be imposed in such a way to change the incentive structure of The Prisoners' Dilemma. But in addition to there being different sorts of incentives and penalties, one of the things that's important to recognize in thinking about this question is that there can also be different sorts of mechanisms of enforcement that are put into play. And this will ultimately bring us to why it is that Hobbes thinks it's required that we have the sort of external force that the government provides.

So we might on the one hand have mechanisms of enforcement that are intrapersonal. We might create within ourselves certain kinds of attitudes that cause us to cultivate cooperative behavior. Conscience is an instance of an intrapersonal solution to coordination problems. You internalize social norms, it becomes part of your self-conception, and as a result, you behave in pro-social ways. It could be in the context of The Tragedy of the Commons. It could be in the context of The Prisoners' Dilemma. It could be in the context of your own cultivation of habits to overcome that intrapersonal, cross-temporal prisoners' dilemma that we all face with regard to the temptations of Angry Birds.

It could be some sort of informal, interpersonal, implicit or explicit schema. So, for example, you might adopt a strategy of cooperating in the first round of a prisoners' dilemma game, and then following the lead of whatever your co-player does, in subsequent rounds of the game. That, as you know from your reading, is called the tit-for-tat strategy. And a supplementary reading, which I will post for you, given the sort of war theme that has run through the course, is a wonderful piece by Robert Axelrod about the evolution of a tit-for-tat strategy in trench warfare during World War I. And that will be up later this afternoon.

So sometimes informal cooperative strategies arise, and either implicitly or explicitly people engage in relatively stable rounds of cooperation. We can put into place formal, interpersonal, formal impersonal, institutional structures. Things like laws, and the state, where there's in position a regulation from an outside force.

And we can finally put in place various kinds of technological controls. Turning off the wireless Internet on your computer. Setting up the missiles during the Cold War so that they fire without human intervention under certain situations. And those two can serve the function of enforcement.

So the ways of getting out of The Prisoners' Dilemma, The Problem of the Commons, are manifold. And they make use of virtually all of the sorts of considerations that we've looked at in class this semester. What I want to close with is by letting you see how much more clearly thinking about things in this way has, I hope, enabled you to understand the final bit of Hobbes that we read for Tuesday's class.

So you'll recall I gave you the first and second laws of nature. That the first law of nature said, make peace where possible, reserve war where necessary. And the second said, lay down your rights exactly to the extent that others are willing to lay down theirs. The third law of nature, says Hobbes, is to perform your covenants, but he points out that you will be unable to follow this law that self-interest demands if you face the live possibility that the other party will renege. Because if that happens you will move from your second choice to your fourth choice. And no one wants to end up there. So, says Hobbes, in order to have covenants which will allow you to thrive and flourish and gain the benefits of cooperation, there must be some sort of enforcement in place. And what Hobbes suggests there must be is a coercive power that compels men equally to the performance of their covenants by the terror of some punishment greater than the benefit they expect by the breach of their covenants.

That is, Hobbes is articulating in the selections that we read from chapter 15 of Leviathan, one of the strategies, which by mathematical analysis of the case, we realized would be sufficient to move people from the three-three cell to the two-two one.

So what we'll look at next week are two different kinds of justifications for various kinds of social structure. We'll look at John Rawls' appeal to our notions of fairness, and Robert Nozick's discussion of the notion of liberty.

And the four of you to whom I owe money are welcome to come up now to obtain it.

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