Large Deviations and Equilibrium Selection in Large Populations

This paper uses the theory of large deviations to analyse equilibrium selection in one-dimensional games with large populations where the system evolves according to a jump Markov process. The equilibria selected maximise a quasi-potential function which can be determined by solving a polynomial equation. Estimates of waiting times are also given. It shows that equilibria about which there is more noise are less likely to be selected and clarifies the role of the limiting deterministic dynamic in selection.