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. In each period, agents are randomly selected to revise actions. They draw a random sample of other agents’ actions, use statistical inference to estimate the action distribution in the population, and choose the best response to the estimate. We show that this dynamic gives rise to a simple aggregate dynamic. The dynamic converges to a Bayesian sampling equilibrium with statistical inference (SESI) if and only if the aggregate dynamic converges to the corresponding state. Furthermore, the set of Bayesian SESIs is globallyasymptotically stable. We discuss the global convergence to a unique Bayesian SESI in anti-coordination games, equilibrium selection in coordination games, a welfare-improving tax scheme, and the extension of heterogeneity to the inference procedures