Rationalization and Identification of Binary Games with Correlated Types

TL;DR

This paper develops a nonparametric framework for analyzing binary games with correlated private types, providing conditions for full and partial identification of payoffs and types, with implications for empirical model testing.

Contribution

It introduces a fully nonparametric approach to rationalize and identify binary games with correlated types, extending existing models to account for correlation and multiple equilibria.

Findings

Model with exogenous payoff shifters is fully identified up to scale and location.

Provides conditions for partial identification under weaker assumptions.

Discusses implications for testing and estimation of binary games.

Abstract

This paper studies the rationalization and identification of binary games where players have correlated private types. Allowing for correlation is crucial in global games and in models with social interactions as it represents correlated information and homophily, respectively. Our approach is fully nonparametric in the joint distribution of types and the strategic effects in the payoffs. First, under monotone pure Bayesian Nash Equilibrium strategy, we characterize all the restrictions if any on the distribution of players' choices imposed by the game-theoretic model as well as restrictions associated with two assumptions frequently made in the empirical analysis of discrete games. Namely, we consider exogeneity of payoff shifters relative to private information, and mutual independence of private information given payoff shifters. Second, we study the nonparametric identification of the payoff functions and types distribution. We show that the model with exogenous payoff shifters is fully identified up to a single location--scale normalization under some exclusion restrictions and rank conditions. Third, we discuss partial identification under weaker conditions and multiple equilibria. Lastly, we briefly point out the implications of our results for model testing and estimation.