题目: Nonparametric Identification of Incomplete Information
2x2 Games without Equilibrium Restrictions
Erhao Xie is a senior economist at the Bank of Canada. He received his PhD in economics from the University of Toronto in 2018. Erhao’s research interests are in Econometrics, Industrial Organization, and Behavioral Economics. In particular, he develops econometric methods to estimate game theoretic models. He also applies these tools to study firm competition in the real world and individual behavior in the laboratory. Erhao’s papers have been published/accepted at the Journal of Business & Economic Statistics, Journal of Economic Behavior & Organization, Journal of Econometric Methods.
In the literature that estimates games with incomplete information, researchers usually impose two restrictions. 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 is allowed to be any probability distribution over the other player's action set. This specification nests the equilibrium restriction when each player's belief corresponds to the other player's actual choice probability. It also allows non-equilibrium behaviors when players' beliefs are biased. Under the above framework, this paper first derives a testable implication of the equilibrium condition. It then provides sufficient conditions for point identification of the payoff function, the belief function, and the distribution of private information.