In this paper we analyze players' long-run behavior in evolutionary coordination games with imperfect monitoring in a large population. Players can observe signals corresponding to other players' unseen actions and use the proposed simple or maximum likelihood estimation algorithm to extract information from the signals. In the simple learning process we find conditions for the risk-dominant and the non-risk-dominant equilibria to emerge alone in the long run. Furthermore, we find that the two equilibria can coexist in the long run. In contrast, the coexistence of the two equilibria is the only limit distribution under the maximum likelihood estimation learning algorithm. We also analyze the long-run equilibria of other 2x2 symmetric games under imperfect monitoring.

This paper analyzes players’ long-run behavior in an evolutionary model with time-varying mutations under both uniform and local interaction rules. It is shown that a risk-dominant Nash equilibrium in a 2 × 2 coordination game would emerge as the long-run equilibrium if and only if mutation rates do not decrease to zero too fast under both interaction methods. The convergence rates of the dynamic system under both interaction rules are also derived. We find that the dynamic system with local matching may not converge faster than that with uniform matching.