Game theory -  A Tutorial

Jean Walrand

Static: Prisoner’s Dilema

Alice and Bob are suspect of a crime and are kept in separate jails. If they both plead innocent (designated by C, for cooperating with each other), then the police believe they are guilty but have only a weak case; they both get 2 years in jail. If Alice accuses Bob (Defects from their partnership) and Bob does not,

Alice gets only one year in jail (for helping the police) and Bob gets 5 years in jail.  The situation is symmetric if Alice cooperates and Bob defects.  If they both accuse each other, they get 4 years each.

This game has only one Nash equilibrium: (D, D). However, under this equilibrium, both players are worse off than if they both cooperate. Selfish behavior is bad for both.