Identification and Estimation of Games with Incomplete Information Using Excluded Regressors

The existing literature on binary games with incomplete information assumes that either payoff functions or the distribution of private information are finitely parameterized to obtain point identification. In contrast, we show that, given excluded regressors, payoff functions and the distribution of private information can both be nonparametrically point identified. An excluded regressor for player i is a sufficiently varying state variable that does not affect other players' utility and is additively separable from other components in i's payoff. We show how excluded regressors satisfying these conditions arise in contexts such as entry games between firms, as variation in observed components of fixed costs. Our identification proofs are constructive, so consistent nonparametric estimators can be readily based on them. For a semiparametric model with linear payoffs, we propose root-N consistent and asymptotically normal estimators for parameters in players' payoffs. Finally, we extend our approach to accommodate the existence of multiple Bayesian Nash equilibria in the data-generating process without assuming equilibrium selection rules.