Semiparametric Analysis of Binary Games of Incomplete Information

This paper studies the identification and estimation in an I-player binary game of incomplete information. Our approach allows players' type to be correlated across players. By focusing on the monotone pure strategy Bayesian Nash Equilibrium (BNE), we show that the equilibrium strategies can be represented as a single-agent binary response model. Under weak restrictions, we show that the distribution of incomplete information can be nonparametrically identified. Further, we establish the identification of payoff functions in a linear-index setup. Following Klein and Spady (1993), we propose a three-stage estimation procedure and show that our estimator is square-root-n consistent, asymptotically normally distributed.