Asynchronous Choice and Markov Equilibria:Theoretical Foundations and Applications

This paper provides a theoretical foundation for Markov (perfect) equilibria in repeated games with asynchronous moves that is based on memory costs. We show that if players incur a ``complexity cost'' which depends on the memory length required by their strategies, then any rationalizable strategy is Markovian. Thus, every Nash or perfect equilibrium is Markovian as well. We also provide a dynamic learning rationale for this conclusion. Our result has interesting implications for repeated asynchronous choice games where the stage game is of common interest. If players are sufficiently patient, rationalizability ensures repeated play of the efficient stage-game equilibrium if this equilibrium satisfies a risk-related condition --- in 2x2 games risk- dominance is a sufficient condition.