Inference in Games Without Equilibrium Restriction: An Application to Restaurant Competition in Opening Hours

Abstract

This article relaxes the Bayesian Nash equilibrium assumption in the estimation of discrete choice games with incomplete information. Instead of assuming unbiased/correct expectations, the model specifies a player’s belief about the behaviors of other players as an unrestricted unknown function. I then study the joint identification of belief and payoff functions in a game where players have different numbers of actions (e.g., 3 × 2 game). This asymmetry in action sets partially identifies the payoff function of the player with more actions. Moreover, if usual exclusion restrictions are satisfied, the payoff and belief functions are point identified up to a scale, and the restriction of equilibrium beliefs is testable. Finally, under a multiplicative separability condition on payoffs, the above identification results are extended to the player with fewer actions and to games with symmetric action sets. I apply this model and its identification results to study the store hours competition between McDonald’s and Kentucky Fried Chicken in China. The null hypothesis of unbiased beliefs is rejected. If researchers incorrectly impose the equilibrium assumption, then the estimated interactive effect would be biased downward by more than 50%.

Keywords:

• Biased beliefs
• Empirical games
• Identification
• Incomplete information
• Store hours

Acknowledgments

This article is based on the first chapter of my Ph.D. thesis at the University of Toronto. I am grateful to my supervisor Victor Aguirregabiria, and thesis committee members Yao Luo, and Ryan Webb. I thank the Editor Christian Hansen, the Associate Editor and two anonymous referees for constructive comments. I also thank to Andres Aradillas-Lopez, Maren Hansen, Zhentong Lu, Lorenzo Magnolfi, Mathieu Marcoux, Ismael Mourifié, Eduardo Souza-Rodrigues, Colin Stewart, Yuanyuan Wan, Ping Xiao, Yu Zhu and seminar participants at the Bank of Canada, Concordia, McGill, Toronto, Tsinghua, Victoria, CEA, DWAE, EARIE, ESEM, IAAE, IIOC, JEI, and YES Yale for helpful discussions. Finally, I thank to Changsong Li and Qinggang Meng for providing detailed industrial insights and data help. The views in this article do not necessarily represent the views of the Bank of Canada.