12.7 The Prisoner’s Dilemma

The prisoner’s dilemma is a scenario in which the gains from cooperation are larger than the rewards from pursuing self-interest. The story behind the prisoner’s dilemma goes like this:

Two co-conspiratorial criminals are arrested. When they are taken to the police station, they refuse to say anything and are put in separate interrogation rooms. Eventually, a police officer enters the room where Prisoner A is being held and says: “You know what? Your partner in the other room is confessing. Your partner is going to get a light prison sentence of just one year, and because you’re remaining silent, the judge is going to stick you with eight years in prison. Why don’t you get smart? If you confess, too, we’ll cut your jail time down to five years, and your partner will get five years, also.” Over in the next room, another police officer is giving the exact same speech to Prisoner B. What the police officers do not say is that if both prisoners remain silent, the evidence against them is not especially strong, and the prisoners will end up with only two years in jail each.

The game theory situation facing the two prisoners is laid out in the table below. To understand the dilemma, first consider the choices from Prisoner A’s point of view. If A believes that B will confess, then A should confess, too, to avoid getting stuck with the eight years in prison. However, if A believes that B will not confess, then A will be tempted to act selfishly and confess, so they only serve one year. The key point is that A has an incentive to confess regardless of what choice B makes! B faces the same set of choices, and thus will have an incentive to confess regardless of what choice A makes. To confess is called the dominant strategy. It is the strategy an individual (or firm) will pursue regardless of the other individual’s (or firm’s) decision. The result is that if prisoners pursue their own self-interest, both are likely to confess, and end up doing a total of 10 years of jail time between them. Alternatively, if they trust that the other will not confess, they each only serve two years.

The game is called a dilemma because if the two prisoners had cooperated by both remaining silent, they would only have had to serve a total of four years of jail time between them. If the two prisoners can work out some way of cooperating so that neither one will confess, they will both be better off than if they each follow their own individual self-interest, which in this case leads straight into longer jail terms.

Combined with the Public Goods Game, the Prisoner’s Dilemma can offer a glimpse into the reasons cheating may have benefited us in the past. What the Prisoner’s Dilemma does not demonstrate is what happens if the scenario happens again. In the first instance, Prisoner A and Prisoner B quickly learn whether or not they can trust each other to remain silent. If one of them breaks that trust, they will both suffer in future exchanges.