Rationalization and Identification of Discrete Games with Correlated Types

This paper studies the rationalization and identification of discrete games where players have correlated private information (i.e. types). Our approach is fully nonparametric. First, under monotone pure strategy Bayesian Nash Equilibrium, we characterize all the restrictions if any on the distribution of players' choices imposed by the game-theoretic model as well as restrictions associated with three assumptions that have been frequently used in the empirical analysis of discrete games. Namely, we consider additive separability of the private information in the payoffs, exogeneity of the payoff shifters relative to the private information, and mutual independence of the private information conditional on the payoff shifters. Second, we study the nonparametric identification of the payoff functions and types distribution under exclusion restrictions and rank conditions. In particular, we show that our structural model is identified up to a location-scale normalization in the separable case. Third, without imposing exclusion restrictions, we characterize the sharp identification region for the payoff functions and types' distribution.