Identification and Estimation of Sequential Games of Incomplete Information with Multiple Equilibria

Abstract

This paper discusses the identification and estimation of game-theoretic models, mainly focusing on sequential games of incomplete information. In most empirical games, researchers cannot observe the exact order of actions played in the game and rely on the assumption of simultaneous actions. My structural modeling generalizes an empirical game to encompass simultaneous and sequential actions as special cases. I specify a sequential game allowing for multiple players in each stage and multiple Perfect Bayesian Nash Equilibria, showing that the structural parameters, including the payoff function parameters, the order of actions, and the equilibrium selection mechanism, are separately identified. The various exclusion restrictions in the finite mixture literature help attain point identification of structural parameters and provide a testable method to verify identification conditions. Next, I consider a Sieve Minimum Distance (SMD) estimator of Ai and Chen (2003) for the structural parameters and verify its asymptotic properties. The Monte Carlo simulations evaluate the performance of the proposed estimator and provide numerical evidence of potential bias under the misspecified order of actions. The empirical application of Walmart and Kmart's entry game demonstrates that retailers compete sequentially in a significant portion of markets.

Keywords: Sequential games, Discrete games of incomplete information, Perfect Bayesian Nash Equilibria, Semiparametric estimation, Sieve Minimum Distance estimator, Multiple equilibria

JEL Classification: C14, C35, C62, C73