Stochastic strategy adjustment in coordination games (Q1865214)

A model of equilibrium selection in coordination games is studied, where the agents from an infinite population stochastically adjust their strategies to changes in their local environment. Instead of playing a perturbed best-response, it is assumed that the agents follow a rule of switching to better strategies with higher probability. Moreover, the agents stay with their strategy in case they successfully coordinate with their local neighbors. The main result is that both strict Nash equilibria of the coordination game correspond to invariant distributions of the process. Hence evolution of the play is not ergodic but instead depends on the initial conditions.