 The Prisoner’s Dilemma illustrates some of the concepts in game theory that can be analyzed using modal logics. Imagine two players that choose to either cooperate or cheat. If both cooperate, they both achieve a reward of 3 points, if they both cheat, they both get nothing, and if one cooperates and the other cheats, the cheater makes off with 5 points and the cooperator gets nothing. If both players are altruistic and motivated to maximize the sum of their rewards, they will both cooperate, as this is the best they can do together. However, they are both tempted to cheat to increase their own reward from 3 to 5. On the other hand, if they are rational, they may recognize that if they cheat their opponent threatens to cheat and leave them with nothing. So cooperation is the best one can do given this threat. And if each thinks the other realizes this, they may be motivated to cooperate. An extended (or iterated) version of this game gives the players multiple moves, that is, repeated opportunities to play and collect rewards. If players have information about the history of the moves and their outcomes, new concerns come into play, as success in the game depends on knowing their opponent’s strategy, and determining (for example) when he/she can be trusted not to cheat. In multi-player versions of the game, where players are drawn in pairs from a larger pool at each move, one’s own best strategy may well depend on whether one can recognize one’s opponents and the strategies they have adopted. (See Grim et. al., 1998 for fascinating research on Interated Prisoner’s Dilemmas.) 