Self-control problems and the folk theorem

This paper generalizes the basic complete information pure-action folk theorem such that it applies when discounting is present-biased and the discount factor between two successive periods increases with the waiting time until the periods are reached. We distinguish between time-consistent decision makers who maximize their initial preferences and time-inconsistent decision makers who maximize their current preferences, and our folk theorem holds for both types. Since discount functions are not assumed to have any specific functional form, decision makers are said to be patient if the sum of the discount factors for all periods is large.