The empirical content of games with bounded regressors

This paper develops a strategy for identification and estimation of complete information games that does not require a regressor that has large support or a parametric specification for the distribution of the unobservables. The identification result uses a nonstandard but plausible condition on the unobservables: the assumption that the joint density of the unobservables of all agents is unimodal in the sense of achieving the global maximum at a unique point. Also, a three-step semiparametric estimator is proposed. Under mild regularity conditions, the estimator is consistent and asymptotically normally distributed. The estimator is nonstandard in the sense that the estimators of the intercept and interaction effect parameters converge at slower than the parametric rate. An intermediate result concerns identification and estimation of the direction of the interaction effect.