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On Asynchronicity of Moves and Coordination

This paper shows that asynchronicity of moves can lead to a unique prediction in coordination games, in an infinite-horizon setting, under certain conditions on off-equilibrium payoffs. In two-player games we derive necessary and sufficient conditions for play ultimately being absorbed in the Pareto dominant Nash equilibrium of the stage game, for every Markov perfect equilibrium. For players patient enough, the condition is that the Pareto dominant Nash equilibrium is also risk dominant, but for lower levels of patience the condition departs from simple risk-dominance. For general n-player symmetric games with patient players, we show that a necessary and sufficient condition for the Pareto dominant Nash equilibrium to be the unique limit outcome in all symmetric Markov perfect equilibrium is a particular generalization of risk-dominance for more than two players. We provide extensions to the unique selection results to all subgame perfect Nash equilibria, and to coordination games in which different players prefer different Nash equilibria of the stage game.