This paper studies a class of dynamic games, called repeated games with asynchronous moves, where not all players may revise their actions in every period. With state-dependent backwards induction, we introduce the concept of effective minimax in repeated games with asynchronous moves. A player's effective minimax value crucially depends on the asynchronous move structure in the repeated game, but not on the player's minimax or effective minimax value in the stage game. Any player's equilibrium payoffs are bounded below by his effective minimax value. We establish a folk theorem: when players are sufficiently patient, any feasible payoff vector where every player receives more than his effective minimax value can be approximated by a perfect equilibrium in the repeated game with asynchronous moves. This folk theorem integrates Fudenberg and Maskin's (1986) folk theorem for standard repeated games, Lagunoff and Matsui's (1997) anti-folk theorem for repeated pure coordination game with asynchronous moves, and Wen's (2002) folk theorem for repeated sequential games.
