Identification of Games of Incomplete Information with Multiple Equilibria and Common Unobserved Heterogeneity

This paper deals with the identification and estimation of discrete games of incomplete information with multiple equilibria when we allow for three types of unobservables for the researcher: (a) payoff-relevant variables that are players' private information; (b) payoff-relevant variables that are common knowledge to all the players; and (c) non-payoff-relevant or "sunspot" variables which are common knowledge to the players. The specification of the payoff function is nonparametric, and the probability distributions of the unobservables is also nonparametric but with finite support (i.e., finite mixture model). We show that if the number of players in the game is greater than two and the number of discrete choice alternatives is greater than the number of mixtures in the distribution of the unobservables, then the model is nonparametrically identified under the same type of exclusion restrictions that we need for identification without unobserved heterogeneity. In particular, it is possible to separately identify the relative contributions of payoff-relevant and "sunspot" type of unobserved heterogeneity to observed players' behavior. We also present results on the identification of counterfactual experiments using the estimated model.