Identification and Estimation of Incomplete Information Games with Multiple Equilibria

Abstract

Multiple equilibria in games pose a big challenge for identification and estimation. Existing literature typically abstracts from multiplicity by assuming that the data is generated by the same equilibrium. Instead of imposing such restrictions, this paper provides a nonparametric identification methodology for finite action games with incomplete information that allow for (possibly) multiple equilibria. The method is applicable to both cross-sectional and panel data. Upon observing players' actions, the identification is achieved in two steps. First, I identify the equilibrium-specific components, such as the number of equilibria, the equilibrium selection probabilities, and individual players' strategies associated with each equilibrium. The identification is feasible by treating the underlying equilibrium as a latent variable and using results from the measurement error literature. Next, I identify the payoff functions nonparametrically with conventional exclusion restrictions. A two-step estimator is then proposed based on this identification method, which performs well based on Monte Carlo evidence. I apply the proposed methodology to study the strategic interaction among radio stations when choosing different time slots to air commercials. The empirical result supports the claim that multiple equilibria do exist across different cities. Moreover, I find that each city exhibits the same equilibrium over time.