An Impossibility Theorem in Repeated Games

Abstract

We prove a negative result in repeated games which shows that a sizable part of the set of feasible individually rational payoffs can never be supported by strategies that are at all robust to players’ discount factors. We find the cutoff defining this region and interpret it as a limit on the ability to punish deviations when future rewards for randomization cannot be finely calibrated. Furthermore, we present a robust folk theorem to support payoffs in the complementary region with “Blackwell-Nash” strategies that remain SPNE at all greater discount factors.