Nonparametric identification of incomplete information: Discrete games with non-equilibrium behaviors

In the literature that estimates discrete games with incomplete information, researchers usually impose two assumptions. First, either the payoff function or the distribution of private information or both are restricted to follow some parametric functional forms. Second, players' behaviors are assumed to be consistent with the Bayesian Nash equilibrium. This paper jointly relaxes both assumptions. The framework non-parametrically specifies both the payoff function and the distribution of private information. In addition, each player's belief about other players' behaviors is also modeled as a nonparametric function. I allow this belief function to be any probability distribution over other players' action sets. This specification nests the equilibrium assumption when each player's belief corresponds to other players' actual choice probabilities. It also allows non-equilibrium behaviors when some players' beliefs are biased or incorrect. Under the above framework, this paper first derives a testable implication of the equilibrium condition. It then obtains the identification results for the payoff function, the belief function and the distribution of private information.