Statistical Inference in Evolutionary Dynamics

We introduce evolutionary dynamics for two-action games where agents with diverse preferences use statistical inference to guide their behavior. We show that the dynamic converges to a Bayesian sampling equilibrium with statistical inference (SESI) and the set of Bayesian SESIs is globally asymptotically stable. We discuss the global convergence to a unique Bayesian SESI in anti-coordination games, a welfare-improving tax scheme, equilibrium selection in coordination games, an application to the diffusion of behavior on networks, and the extension to multi-action games.