A folk theorem for asynchronously repeated games

We prove a Folk Theorem for asynchronously repeated games in which the set of players who can move in period t, denoted by I,, is a random variable wh ose distribution is a function of the past action choices of the players an d the past realizations of I-tau's, tau = 1, 2,...,t-1. We impose a conditi on, the finite periods of inaction (FPI) condition, which requires that the number of periods in which every player has at least one opportunity to mo ve is bounded. Given the FPI condition together with the standard nonequiva lent utilities (NEU) condition, we show that every feasible and strictly in dividually rational payoff vector can be supported as a subgame perfect equ ilibrium outcome of an asynchronously repeated game.