Identification and Estimation of Incomplete Information Games with Multiple Equilibria∗

The presence of multiple equilibria in games is a big challenge for identification and estimation. Without information of the equilibrium selection, it is impossible to perform counterfactual analysis. Allowing for possibly multiple equilibria, this paper provides nonparametric identification of finite games with incomplete information. Upon observing players’ actions from cross-sectional games, the identification is achieved in two steps. First I identify the equilibrium-specific components, such as the number of equilibria, the equilibrium selection mechanism, and all strategies associated with each equilibrium. In particular, the econometric structure resembles that in measurement error models if I index the underlying equilibria and treat the index as a latent variable, and therefore, these equilibrium-specific components can be identified using results from measurement error literature. Next I identify the payoff functions with exclusion restrictions. This paper proves identification for both static and dynamic settings. Specifically, identification in static games requires at least three players with the standard assumption of independent private shocks, while identification in dynamic games requires four periods of data if only Markov Perfect Equilibria are considered. I apply this methodology to study the strategic interaction among radio stations when choosing different time slots to air commercials. The empirical results show the existence of two equilibria in smaller markets, and these markets exhibit the same equilibrium over time. JEL Classification: C14