Equilibrium Selection with Payoff-Dependent Mistakes

This paper studies equilibrium selection via stochastic dynamics in the style of Young (Econometrica 61, 1993, 57-84), when the mistake probabilities are allowed to depend on their expected payoffs. Although any strict equilibrium can be selected with properly constructed state-dependent mistakes (Bergin and Lipman, Econometrica, 64, 1996, 943-956), reasonable assumptions on state dependence could produce a consistent equilibrium selection. The main analysis shows how payoff dependency and payoffs interact to determine a long-run equilibrium and characterizes the selection relating to the traditional notions of risk dominance, payoff dominance, and maxmin in 2x2 games