Learning to Forgive

The Folk Theorem for infinitely repeated games offers an embarrassment of riches; nowhere is equilibrium multiplicity more acute. This paper selects amongst these equilibria in the following sense. If players learn to play an infinitely repeated game using classical hypothesis testing, it is known that their strategies almost always approximate equilibria of the repeated game. It is shown here that if, in addition, they are sufficiently conservative in adopting their hypotheses, then almost all of the time is spent approximating an efficient subset of equilibria that share a forgiving property. This result provides theoretical justification for the general sense amongst practitioners that efficiency is focal in such games.