Repeated Games with Present-Biased Preferences

We study infinitely repeated games with perfect monitoring, where players have beta-delta preferences. We compute the continuation payoff set using recursive techniques and then characterize equilibrium payoffs. We then explore the cost of the present-time bias, producing comparative statics. Unless the minimax outcome is a Nash equilibrium of the stage game, the equilibrium payoff set is not monotonic in beta or delta. Finally, we show how the equilibrium payoff set is contained in that of a repeated game with smaller discount factor