Tid: 11 april 2011 kl 15.15-16.00.

Föredragshållare: William H. Sandholm

Titel: Large Deviations, Reversibility, and Equilibrium Selection under Evolutionary Game Dynamics

Abstract We consider a general model of stochastic evolution in games in which agents employ myopic decision rules, studying the asymptotics of behavior in the large population limit over various time scales. Existing analyses obtain deterministic approximations of finite-horizon behavior in terms of mean dynamics, and descriptions of infinite-horizon behavior and stochastic stability via limiting stationary distributions. To complement these analyses, and to explain the relations between them, we provide a large deviations analysis, which describes the probabilities of excursions against the flow of the mean dynamic over intermediate time scales. This "local" large deviations analysis is combined with graph theoretic methods to obtain conclusions about the "global" behavior of the process, in particular, the asymptotics of the stationary distribution and the expected times until exit from general domains. Detailed analyses are provided for two settings: potential games under the logit choice rule, and two-strategy games under arbitrary choice rules. In both cases, the large deviations analysis reveals that the processes are "reversible in the large", providing a powerful new approach to understanding global behavior in these settings.

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