Hobbes and the Prisoner's Dilemma

I The State of Nature as a Prisoners' Dilemma

II Modifications of the Dilemma

III Other Solutions to Cooperation

I The State of Nature as a Prisoners' Dilemma

The dilemma Hobbes saw was the problem of how we can achieve the benefits of trust. Why not trust people? Why can't we cooperate, even though we are self-interested, since cooperation, if others also cooperate, is in everybody's interests?

A model of the difficulty is what is called the Prisoners' Dilemma:

Suppose you and a friend have committed a crime together, and the police suspect you, but don't have proof [and are unlikely to get it]

Suppose the police offer you the following deal:

If you confess to the joint crime, and your buddy does not, you'll get off sot-free, whereas he will get a 15 year sentence.

If you both confess, you'll both get 10 year sentences.

If neither of you confess, you'll both get three-year sentences. You are aware that your buddy has been offered the same deal.

So, what do you do?

A grid will clarify the situation. Suppose you are A and your buddy is B.

A's options are the vertical column; B's options the horizontal. There are four possibilities, and four different outcomes [A's,B's] in the four possibilities.

B quiet B confesses

A quiet ║ A B ║ A B

║ - 3, - 3 ║ -15, 0

___________________________

A confesses ║ A B ║ A B

║ 0, -15 ║ -10, -10

Whether or not B confesses, A is better off confessing. So, it is in A's interest to confess.

But the same is true of B. But then, they are both worse off (10 years in prison) than they would be if neither confessed.

Could cooperation help? Of course. But how can you bring about cooperation? Suppose A and B are allowed to confer before they meet again with the police to either make their confessions or not. Suppose they promise one another to both confess. The situation doesn't change very much. There is little reason to think that they will keep their promises. After all, keeping your (A's) promise and keeping quiet will cost you (A) either 2 extra years in prison, if B also keeps quiet, or an extra 14 years in prison, if B confesses, breaking his word. In fact, if B is like A, he would be foolish to keep his promise.

What the situation needs is not only contracts and promises, but somebody or something to enforce the keeping of promises/ contracts. Suppose you record your promise with the Mafia, which has the means to punish criminals who break their promises to each other. The existence of an enforcer of contracts makes contracts possible and reliable. You know that B will keep up his end of the bargain, since he is rational and fears the punishment the Mafia will enforce if he doesn't keep his part of the bargain.

The enforcement by the Mafia is effective to the extent that the Mafia has power. The Mafia has power only to the extent that people are willing to do the dirty work it instructs. So, for instance, both A and B, assuming that they are criminals and members of the Mafia, would sometimes have to go out and do some enforcement. In that case, they would have given up their rights to do what they choose and transferred those rights to the Mafia. The reason they would have transferred those rights is their own self-interest. It is in their interests to be able to make contracts that are meaningful, and this is the only way to do it. You have to have an effective enforcer of contracts in order to make contracts that are beneficial to yourself.

Hobbes would say that in this case, you act unjustly, since you have promised. However, "nothing is easier than breaking your word." So how can promises be really binding?

The situation in Hobbes' state of nature is like the Prisoners' Dilemma: By acting solely on self-interest, you and the other people end up in a situation that is worse for everyone than an alternative possible outcome that you could have reached. The problem is how, given that people are naturally driven to seek their own self-interest, can you reach this better solution? Hobbes' answer is that the people can contract among themselves to give all power to a Sovereign, who will then have an interest in enforcing contracts, and in passing laws prohibiting aggression among citizens, since a population that prospers makes the sovereign stronger, and a population that has "the social contract" will prosper, relatively speaking.

The state of nature is much like a Prisoners' Dilemma. You and everyone else wants peace, but given the nature of human beings as self-interested, there is no way to get peace. If you act in a trusting way, and don't attack potential attackers first, you'll be taken advantage of and killed or enslaved. In a situation where you don't attack potential attackers, it will be in their self-interest to attack you. Then they get your stuff, and they get to survive.

Just to emphasize this resemblance, consider A and B to be two people in the state of nature. If they spend the effort to prepared attacking and being attacked by the other, their own work and food-production suffers. If they don't spend this effort, and get attacked, they suffer a great deal more. The ideal situation would be that they don't prepare for attacks, and neither attacks the other. But if the other person is not prepared, both A and B are better off attacking.

B relaxes B prepares

A relaxes ║ A B ║ A B

║ - 3, - 3 ║ -15, 0

___________________________

A prepares ║ A B ║ A B

║ 0, -15 ║ -10, -10

What makes this a prisoner's dilemma is that no matter what B does, A is better off preparing; and whatever A does, B is better off preparing.

Note that solemn promises will not help, because now the question is whether to keep your promise, and the same matrix arises:

B keeps B breaks

A keeps ║ A B ║ A B

║ - 3, - 3 ║ -15, 0

___________________________

A breaks ║ A B ║ A B

║ 0, -15 ║ -10, -10

II Applications of the Dilemma

Prisoners' Dilemmas and other game-theoretic models explain a lot about social facts. Take a mugging in public, where two or three youths rob an individual in plain sight of a crowd. What do you do? If you act and nobody else does, probably the result will be that you get robbed as well, at best. The ideal situation is that many other people in the crowd would join you in defeating the muggers. IF you knew that many other people would join you, then it would be better for everyone that you attack the muggers. But if you knew that, so would the muggers. The most likely outcome of a situation in which everyone was willing to come to someone else's assistance in a somewhat dangerous situation is that such muggings would not take place. No muggings would happen in a situation in which it is widely known that this will be the response.

When a society can develop dispositions that depend on trust in one's fellows, great benefits accrue. When a society is falling apart, or when you don't really have a society, everyone has to "look out for himself" there is no trust in others to take certain kinds of actions, and everybody loses.

What is going on in this kind of situation? How does it arise that dispositions to aid each other come into existence? For one thing, there are sanctions and threats to a person NOT intervening. In a society where people are expected to come to one another's aid, people are punished for not helping each other, for not taking risks when someone else needs help. You'll have a reputation as a coward, for instance. Your acquaintances will treat you with contempt. They won't join with you in projects.

What has to exist for this situation to arise?

1) First, there have to be repeated situations, rather than a single unique event. People take risks on the basis of past experience.

2) Second, the knowledge of the behavior of the actors in previous situations is brought to bear in the new situations. If you have a number of people who know that their fellows will join in, the rationality of taking a risky action is increased.

3) Third, there have to be sanctions on defections. What happens when a person doesn't join in, or breaks a promise? Why don't people generally break promises? The main difficulty with breaking promises is a reputation for breaking promises. [The same thing applies to lying.] Damaging your reputation basically means having other people know that you will not be reliable. Thus your ability to benefit by future promises is compromised by breaking your promise in a given situation.

In the original prisoners' case in which the prisoners are allowed to confer and make promises, if we imagine that this situation happens again and again, getting busted on, say, drug-possession charges, where the penalties are in days rather than years, criminals will get reputations for keeping promises or violating them. So, the cost of "looking out for number 1" in a given situation will be future difficulties. If you become known as someone who is unreliable, you will find yourself in the "10.10" box a lot of the time in the future.

On the other hand, if you take the "irrational" action of keeping your promise, other criminals will find out that you keep your promises and you can arrive at the "3,3" optimal solution for both of you, given that you both want to have reputations as promise keepers. If you have information about what people have done in the past, the complexion of the decision changes, even without an enforcer. [In effect, the rest of the criminals themselves become enforcers, either by refusing to believe your promises, thus sticking you in the "10,10" box or by treating you with contempt or breaking your legs.]

How does this work in the long run? Suppose you limit "punishments" to refusals to believe promises. Suppose also that you limit information to how a given person has behaved toward YOU. (So you don't know the person's over-all track record.) The main problem with keeping promises is that you can be taken advantage of. If the other person knows you are a "sucker" who will keep promises all the time with anyone no matter what, then there is no reason not to take advantage of you.

If you limit people's information to "how has the person behaved with ME" in the past, it turns out that a very good strategy is "tit for tat": You trust people if and only if they were trustworthy the last time. That is, you "forgive" defections on the basis of one case of promise-keeping. This strategy actually turns out to pay off in many, many cases in the long run, at least in computer simulations. But other strategies work better in other [artificial] situations.

Notice that the limitations of this model make it pretty abstract and unreal. You have to suppose that people's over-all track-records are unknown. You have to imagine that there is no continuing relationship among the actors separate from the particular actions.

III The "Iterated Prisoner's Dilemma Solution to the Problem of Cooperation

Hobbes thinks that only an absolute power over everyone, given to some person or group of persons, will keep an individual safe.

So, Hobbes thinks that "savage" peoples live in "states of nature", since they by and large have no absolute monarchs. Hobbes was mistaken on both points. Cooperation is possible in situations where there are repeated encounters/ transactions between agents who have experience with one another. In a small society, while there are prisoners' dilemma situations, they are repeated again and again. In a small society, by and large people know each other, and remember previous encounters.

Hobbes' "war of all against all" scenario only applies to ONE-TIME encounters between strangers.

Given repeated (iterated) prisoners' dilemma situations, with individual players reidentifying each other, then cooperation can emerge. In fact, cooperation turns out to be self-interested by all parties. A simple strategy, which we will talk about at some length, can bring about cooperation. This is the strategy of cooperating unless the other person defected last time. Following Axelrod, call this strategy "TIT FOR TAT." Someone following TFT begins by cooperating, and returns a defection with a retaliatory defection. When the other person acts cooperatively, you cooperate also. (You "forgive.") This is the simple strategy of doing whatever the other person did the last time.

Suppose we have the original situation, but with fines being paid rather than years in prison. Each person gets -3 if both cooperate, 0 and -15 or -15 and 0 if one cooperates and the other does not, and -10 each if they both defect. If A consistently does what the other person did before, and B defects the first time, then B will end up with an initial 0, but a long line of -10's.

Consider A's and B's score after 10 runs:

Run 1 2 3 4 5 6 7 8 9 10

A -15 -10 -10 -10 -10 -10 -10 -10 -10 -10 = -105

B 0 -10 -10 -10 -10 -10 -10 -10 -10 -10 = - 90

If B had cooperated, the scores would have been -30 apiece, or three times as good, EVEN FOR B. Notice that B has "won", in the sense that B has done better than A, but B is still much worse off than he could have been.

So B's total "score" of fines paid will be far more than it could have been if he cooperated. If B knows that A will retaliate, and the relationship is enduring, then it is in B's interest to cooperate. Since tit for tat is so simple, B can easily find out that that is A's strategy. As soon as B realizes this, B will also realize that lack of cooperation is hurting himself.

Suppose B realizes that A is retaliating after the third run, and decides to cooperate twice in a row to see if A will forgive. From that point on, both A and B do better.

Run 1 2 3 4 5 6 7 8 9 10

A -15 -10 -10 0 -3 -3 -3 -3 -3 -3 = -53

B 0 - 10 -10 -15 -3 -3 -3 -3 -3 -3 = -53

In situations where there is repeated prisoner's dilemma type interaction among agents who can identify one another and remember past experience with them, cooperation can emerge. Cooperation actually does emerge, it turns out [multiple experiments and anecdotes] without any central authority. Given that people retaliate after they are betrayed, but are willing to forgive a betrayal, cooperation can emerge from people seeking their own interests.

[Some other comments: Since everyone wants other people to cooperate, and people realize that the only way to foster cooperation is to punish the non-cooperative, people will begin to punish non-retaliators. So, for instance, you will be punished for knowingly permitting a theft to occur. When non-retaliation is itself punished, we begin to have NORMS emerge. People are expected to (and coerced to) respond to defections with retaliation. ]