Inference for Games with Many Players

We develop an asymptotic theory for static discrete-action games with a large number of players, and propose a novel inference approach based on stochastic expansions around the limit of the finite-player game. Our analysis focuses on anonymous games in which payoffs are a function of the agent's own action and the empirical distribution of her opponents' play. We establish a law of large numbers and central limit theorem which can be used to establish consistency of point or set estimators and asymptotic validity for inference on structural parameters as the number of players increases. The proposed methods as well as the limit theory are conditional on the realized equilibrium in the observed sample and therefore do not require any assumptions regarding selection among multiple equilibria.