An `Anti-Folk Theorem' in Asynchronously Repeated Games


The standard model of repeated games assumes perfect synchronization in the timing of decisions between the players. In many natural settings, however, choices are made asynchronously so that only one player can move at any given time. This paper studies a family of repeated settings in which choices are asynchronous. Initially, we examine, as a canonical model, a simple two person alternating move game. There, it is shown that for sufficiently patient players, every Perfect equilibrium payoff comes arbitarily close to the Pareto dominant payoff if the stage game is one of pure coordination. The result generalizes to any finite number of players and any game in a class of {\it asynchonrously repeated games} which includes both stochastic and deterministic repetition. It also holds for repeated settings in which the timing of moves is endogenous.
The results complement a recent Folk Theorem result by Dutta (1995) for stochastic games which can be applied to asynchronously repeated games if a full dimensionality condition holds. However, because the minimax benchmark in an asynchronously repeated game may be different than for a standard repeated game, the form of multiplicity will in general be different for the two. With asynchronous choice, the Folk Theorem multiplicity is also sensitive to the order of limits. A standard Folk Theorem fixes the stage game and varies the discount factor. If it is the other way around, then the ``Anti-Folk Theorem" holds in generic games. In other words, for any fixed discount factor close to one, the optimality result holds for a neighborhood of pure coordination games.
Journal of Economic Literature Classification Numbers: C72, C73.
Keywords: repeated games, asynchronously repeated games, alternating move games, pure coordination games, stochastic games.