Identification and Estimation of Games with Incomplete Information Using Excluded Regressors, Second Version

We show nonparametric point identification of static binary games with incomplete information, using excluded regressors. An excluded regressor for player ¡ is a state variable that does not affect other players’ utility and is additively separable from other components in ¡’s payoff. When excluded regressors are conditionally independent from private information, the interaction effects between players and the marginal effects of excluded regressors on payoff are identified. In addition, if excluded regressors vary sufficiently relative to the support of private information, then the full payoff functions and the distribution of private information are also nonparametrically identified. We illustrate how excluded regressors satisfying these conditions arise in contexts such as entry games between firms, as variation in observed components of fixed costs. We extend our approach to accommodate the existence of multiple Bayesian Nash equilibria in the data-generating process without assuming equilibrium selection rules. For a semiparametric model with linear payoff, we propose root-N consistent and asymptotically normal estimators for parameters in players’payoffs.