Game Theory

Repeated Prisoner's Dilemma

In repeated Prisoner's Dilemmas, players are better off not following their dominant strategies. Instead, they minimize their prison time by following a tit-for-tat strategy.
The Prisoner's Dilemma suggests that criminals should have dominant strategies (strategies that give the best outcome regardless of the other player's choice) to confess when offered a deal by the police, yet this isn't always the case in the real world. First, the payoff matrix assumes that the only thing that matters to these players is the number of years they will spend in prison. Criminals likely care about other factors as well, including their reputation or a possible threat of retaliation from the other player. Furthermore, the game described is a one-period game. It is played, the players receive their payoffs (prison sentences), and the game ends, which is not very realistic.

The Prisoner's Dilemma could be played over and over by the same players. In that case, when making the decision of whether to turn against the other in return for a lighter sentence, each player must consider the possibility of retaliation. The possibility of retaliation changes the dynamics a great deal.

Political scientist Robert Axelrod once held a Prisoner's Dilemma tournament to see what strategy works best when the game is played numerous times. The winning strategy (in which players received the lowest number of years in prison) is called a tit-for-tat strategy. Players start out cooperating with opponents and then play the option the opponent played in the round before. Here, player 1 denies in the first round. In the next round (and all future rounds), player 1 opts for the choice made by player 2 in the previous round. Therefore, if player 2 also chooses to deny, both players can limit the total amount of jail time they get. Only after player 2 confesses does player 1 confess in the next round. If player 2 goes back to denying involvement in the drug trade, player 1 will deny in the next round as well. It's as if player 1 will punish player 2 for selling him or her out but will then forgive player 2 if he or she goes back to denying any involvement.
In the tit-for-tat scenario, player 1 (Jesse) chooses to deny in the first round. In all subsequent rounds, Jesse chooses the strategy Walter chose in the previous round. It's as if Jesse punishes Walter for confessing but forgives him for denying involvement.