Game Theory Course: 5.3 A Folk Theorem Sampler

Jim Ratliff

Game Theory

Repeated Games

Article

The original motivation for developing a theory of repeated games was to show that cooperative behavior was an equilibrium. The theoreticians were all too clever, for, as we will see, they showed that in many cases a huge multiplicity of even very "noncooperative" stage-game payoffs could be sustained on average as an equilibrium of the repeated game. These findings are made precise in numerous folk theorems. Each folk theorem considers a class of games and identifies a set of payoff vectors each of which can be supported by some equilibrium strategy profile. There are many folk theorems because there are many classes of games and different choices of equilibrium concept. Some folk theorems identify sets of payoff vectors which can be supported by Nash equilibria; of course, of more interest are those folk theorems which identify payoffs supported by subgame-perfect equilibria.