Game Theory Course: 5.1 Introduction to Repeated Games

Jim Ratliff

Game Theory

Repeated Games

Article

One striking feature of many one-shot games we study (e.g., the Prisoners' Dilemma) is that the Nash equilibria are so noncooperative: each player would prefer to fink than to cooperate. Repeated games can incorporate phenomena which we believe are important but which aren't captured when we restrict our attention to static, one-shot games. In particular we can strive to explain how cooperative behavior can be established as a result of rational behavior. We will develop a useful formalism, the semiextensive form, for analyzing repeated games, i.e. those which are repetitions of the same one-shot game (called the stage game). We will describe strategies for such repeated games as sequences of history-dependent stage-game strategies. The payoffs to the players in this repeated game will be functions of the stage-game payoffs. We will define the concept of Nash equilibrium and after identifying the subgames in this formalism the concept of a subgame-perfect equilibrium for a repeated game.