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.