Identification and estimation of games with incomplete information using excluded regressors

We show structural components in binary games with incomplete information are nonparametrically identified using variation in player-specific excluded regressors. An excluded regressor for a 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. Such excluded regressors arise in various empirical contexts. Our identification method is constructive, and provides a basis for nonparametric estimators. For a semiparametric model with linear payoffs, we propose root-N consistent and asymptotically normal estimators for players' payoffs. We also discuss extension to the case with multiple Bayesian Nash equilibria in the data-generating process without assuming equilibrium selection rules.