Inference for Games with Many Players

We develop an asymptotic theory for static discrete games (“markets”) with a large number of players, and propose a novel approach to inference based on stochastic expansions around a “competitive” limit of the finite-player game. We show that in the limit, players’ equilibrium actions in a given market can be represented as a mixture of i.i.d. random variables, where for common specifications identification of structural parameters from the limiting distribution is analogous to static panel models of discrete choice. Our analysis focuses on aggregate games in which payoffs depend on other players’ choices only through a finite-dimensional aggregate state at the market level. We establish conditional laws of large numbers and central limit theorems 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. Our results cover games with complete information or private types, as well as intermediate cases, and allow for arbitrary mechanisms for selecting among multiple equilibria. JEL Classification: C12, C13, C31, C35, C72