Folk Theorems for Present-Biased Players

The folk theorems for infinitely repeated games with discounting presume that the discount rate between two successive periods is constant. Following the literature on quasi-exponential or hyperbolic discounting, I model the repeated interaction between two or more decision makers in a way that allows present-biased discounting where the discount factor between two successive periods increases with the waiting time until the periods are reached. I generalize Fudenberg and Maskin's (1986) and Abreu, Dutta and Smith's (1994) folk theorems for repeated games with discounting so that they apply when discounting is present-biased. Patience is then represented either by the discount factor between the next and the current period or, alternatively, by the sum of the discount factors for all future periods.