Large Deviations and Stochastic Stability in the Small Noise Double Limit, II: The Logit Model

We describe the large deviations properties, stationary distribution asymptotics, and stochastically stable states of stochastic evolutionary processes based on the logit choice rule, focusing on behavior in the small noise double limit. These aspects of the stochastic evolutionary process can be characterized in terms of solutions to certain minimum cost path problems. We solve these problems explicitly using tools from optimal control theory. The analysis focuses on three-strategy coordination games that satisfy the marginal bandwagon property and that have an interior equilibrium, but our approach can be applied to other classes of games and other choice rules.