The Prisoner’s Dilemma and Strict Dominance

Two thieves plan to rob an electronics store. As they approach the backdoor, the police arrest them for trespassing. The cops suspect that the pair planned to break in but lack the evidence to support such an accusation. They therefore require a confession to charge the suspects with the greater crime.

Having studied game theory in college, the interrogator throws them into the prisoner’s dilemma. He individually sequesters both robbers and tells each of them the following:

We are currently charging you with trespassing, which implies a one month jail sentence. I know you were planning on robbing the store, but right now I cannot prove it—I need your testimony. In exchange for your cooperation, I will dismiss your trespassing charge, and your partner will be charged to the fullest extent of the law: a twelve month jail sentence. I am offering your partner the same deal. If both of you confess, your individual testimony is no longer as valuable, and your jail sentence will be eight months each. If both criminals are self-interested and only care about minimizing their jail time, should they take the interrogator’s deal?

Looking at the game matrix, people see that the outcome leaves both players better off than the outcome. They then wonder why the players cannot coordinate on keeping quiet. But as we just saw, promises to remain silent are unsustainable. Player 1 wants player 2 to keep quiet so when he confesses he walks away free. The same goes for player 2. As a result, the outcome is inherently unstable. Ultimately, the players finish in the inferior (but sustainable) outcome.