Rationalization and Identification of Discrete Games with Correlated Types
Author(s): Nianqing Liu, Quang Vuong, and Haiqing Xu
Date: April 2014
Type: CRATE Working Papers, CRATE-2014-1
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This paper studies the rationalization and identification of discrete games where players have correlated private information/types. Allowing for correlation across types is crucial, for instance, in models with social interactions as it represents homophily. 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 three assumptions frequently used in the empirical analysis of discrete games. Namely, we consider additive separability of private information, 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. In particular, we show that the model with exogenous payoff shifters and separable private information is fully identified up to a single location–scale normalization under some exclusion restrictions and rank conditions. Third, we discuss partial identification, multi–dimensional types and multiple equilibria. Lastly, we briefly point out the implications of our results for model testing and estimation.