A folk theorem for stochastic games with infrequent state changes

We characterize perfect public equilibrium payoffs in dynamic stochastic games in the case where the length of the period shrinks, but players' rate of time discounting and the transition rate between states remain fixed. We present a meaningful definition of the feasible and individually rational payoff sets for this environment, and we prove a folk theorem under imperfect monitoring. Our setting differs significantly from the case considered in previous literature (Dutta 1995, Fudenberg and Yamamoto 2011, and Horner et al. 2011) where players become very patient. In particular, the set of equilibrium payoffs typically depends on the initial state.