Estimation of Bayesian Nash Equilibria in Two-player Games with Correlated Private Signals

This paper studies a 2×2 static game of incomplete information. I allow players’ private signals to be correlated, which adds complexity to Bayesian Nash Equilibrium (BNE) solutions of the game. Further, the econometric structure of this model is “incomplete” (Tamer, 2003). I therefore focus on a nontrivial subset, Π2(θ0), of the support of public information variables where a unique Monotone Strategy Bayesian Equilibrium (MSBE) exists. I propose a four–step procedure to estimate the payoff structure. In the first step I estimate a set of parameters containing the underlying parameter of interest, θ0. I then obtain a consistent point estimator of θ0. The third step estimator is root n consistent and the final step estimator is more efficient than the third step one.