The prisoner’s dilemma as a briefcase exchange

Game Theory

For our purposes, a game is an interactive situation in which individuals, called players, choose strategies to deal with each other in attempting to maximize their individual utility. There are several ways of distinguishing games including: 1) in respect to the number of players involved; 2) in respect to the number of repetitions of play; 3) in respect of the order of the various player’s preferences over the same outcomes. On the one extreme are games of pure conflict, so-called zero-sum games, in which players have completely opposing interests over possible outcomes. On the other extreme are games of pure harmony, so-called games of coordination. In the middle are games involving both conflict and harmony in respect of others. It is one particular game that interests us most, since it describes the situation in Hobbes’ state of nature, and is the central problem in contractarian moral theory.

The Prisoner’s Dilemma

The prisoner’s dilemma is one of the most widely debated situations in game theory. The story has implications for a variety of human interactive situations. A prisoner’s dilemma is an interactive situation in which it is better for all to cooperate rather than for no one to do so, yet it is best for each not to cooperate, regardless of what the others do.

In the classic story, two prisoners have committed a serious crime but all of the evidence necessary to convict them is not admissible in court. Both prisoners are held separately and are unable to communicate. The prisoners are called separately by the authorities and each offered the same pro-position. Confess and if your partner does not, you will be convicted of a lesser crime and serve one year in jail while the unrepentant prisoner will be convicted of a more serious crime and serve ten years. If you do not confess and your partner does, then it is you who will be convicted of the more serious crime and your partner of the lesser crime. Should neither of you confess the penalty will be two years for each of you, but should both of you confess the penalty will be five years. In the following matrix, you are the row chooser and your partner the column chooser. The first number in each parenthesis represents the “payoff” for you in years in prison, the second number your partner’s years. Let us assume each player prefers the least number of years in prison possible. In matrix form, the situation looks like this:

Prisoner 2

Confess Don’t Confess Prisoner 1 Confess (5, 5) (1, 10) Don’t Confess (10, 1) (2, 2)

So you reason as follows: If your partner confesses, you had better confess because if you don’t you will get 10 years rather than 5. If your partner doesn’t confess, again you should confess because you will only get 1 year rather than 2 for not confessing. So no matter what your partner does, you ought to confess. The reasoning is the same for your partner. The problem is that when both confess the outcome is worse for both than if neither confessed. You both could have done better, and neither of you worse, if you had not confessed! You might have made an agreement not to confess but this would not solve the problem. The reason is this: although agreeing not to confess is rational, compliance is surely not rational!

The prisoner’s dilemma describes the situation that humans found themselves in in Hobbes’ state of nature. If the prisoners cooperate, they both do better; if they do not cooperate, they both do worse. But both have a good reason not to cooperate; they are not sure the other will! We can only escape this dilemma, Hobbes maintained, by installing a coercive power that makes us comply with our agreements (contracts). Others, like the contemporary philosopher David Gauthier, argue for the rationality of voluntary non-coerced cooperation and compliance with agreements given the costs to each of us of enforcement agencies. Gauthier advocates that we accept “morals by agreement.”

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