# The Prisoner's Dilemma

Posted on

## Game Theory and Interdependent Outcomes

Game theory is the study of interdependent decision making, or how individuals make decisions when their optimal choice depends on what others have chosen. Probably the best known application of game theory is the Prisoner’s Dilemma. In this game, there is a tension between the incentives faced by each player and the globally optimal outcome. In the parlance of game theory, Nash equilibrium is not Pareto optimal. Nash equilibrium means that each decision maker cannot do better given what every other decision maker has chosen. Pareto optimality means that no one decision maker can do better without making another worse off.

The Prisoner’s Dilemma gets its name from the following set-up. Two criminals are caught robbing a store and are brought to the police station. The crime is punishable by three months in prison, but the police also suspect each criminal of being involved in another crime that is punishable by three additional months in prison. The police try to get them to confess to the second crime by interrogating the criminals separately. Each prisoner is independently told that he will get leniency on the theft charge if he turns the other in. If both refuse to confess, the cops will not be able charge either for the second crime. If both confess, they’ll each get extra time for the second crime minus one month for their helpful confession. If one confesses, but not the other, the confessor will get five months off the total time while the other serves the full time.

The potential outcomes can be defined in terms of a 2 x 2 payoff matrix like the following, where the numbers indicate the reduced time in prison (meaning higher values are better for the prisoner):