Bounded memory Folk Theorem

We show that the Folk Theorem holds for n-player discounted repeated games with bounded memory (recall) strategies. Our main result demonstrates that any payoff profile that exceeds the pure minmax payoff profile can be approximately sustained by a pure strategy finite memory subgame perfect equilibrium of the repeated game if the players are sufficiently patient. We also show that the result can be extended to any payoff profile that exceeds the mixed minmax payoff profile if players can randomize at each stage of the repeated game. Our results requires neither time-dependent strategies, nor public randomization, nor any communication. The type of strategies we employ to establish our result turn out to have new features that may be important in understanding repeated interactions.