14.2. Prisoner’s Dilemma¶
The Prisoner’s Dilemma is a topic in game theory, but it’s not the fun kind of game. Instead, it is the kind of game that sheds light on human motivation and behavior.
Two members of a criminal gang are arrested and imprisoned. Each prisoner is in solitary confinement with no means of communicating with the other. The prosecutors lack sufficient evidence to convict the pair on the principal charge, but they have enough to convict both on a lesser charge. Simultaneously, the prosecutors offer each prisoner a bargain. Each prisoner is given the opportunity to either: (1) betray the other by testifying that the other committed the crime, or (2) cooperate with the other by remaining silent. The offer is:
If A and B each betray the other, each of them serves 2 years in prison.
If A betrays B but B remains silent, A will be set free and B will serve 3 years in prison (and vice versa).
If A and B both remain silent, both of them will only serve 1 year in prison (on the lesser charge).
Obviously, this scenario is contrived, but it is meant to represent a variety of interactions where agents have to choose whether to “cooperate” with each other or “defect”, and where the reward (or punishment) for each agent depends on what the other chooses.
With this set of punishments, it is tempting to say that the players should cooperate, that is, that both should remain silent. But neither agent knows what the other will do, so each has to consider two possible outcomes. First, looking at it from A’s point of view:
If B remains silent, A is better off defecting; she would go free rather than serve 1 year.
If B defects, A is still better off defecting; she would serve only 2 years rather than 3.
No matter what B does, A is better off defecting. And because the game is symmetric, this analysis is the same from B’s point of view: no matter what A does, B is better off defecting.
In the simplest version of this game, we assume that A and B have no other considerations to take into account. They can’t communicate with each other, so they can’t negotiate, make promises, or threaten each other. And they consider only the immediate goal of minimizing their sentences; they don’t take into account any other factors.
Under those assumptions, the rational choice for both agents is to defect. That might be a good thing, at least for purposes of criminal justice. But for the prisoners, it is frustrating because there is, apparently, nothing they can do to achieve the outcome they both want. And this model applies to other scenarios in real life where cooperation would be better for the greater good as well as for the players.
Studying these scenarios, and ways to escape from the dilemma, is the focus of people who study game theory, but it is not the focus of this chapter. We are headed in a different direction.