Testing Collusion and Cooperation in Binary Choice Games

This article studies binary choice games with complete information and proposes a test for the null hypothesis of collusion / cooperation, where players coordinate their actions to maximize the weighted sum of all players' payoffs. Consider an arbitrary game, referred to as the original game. With data on players' actual choices and under weak regularity conditions, I show that the collusive model of the original game is observationally equivalent to an equilibrium model of a transformed game with an alternative payoff structure. Notably, this equivalent equilibrium model must satisfy two key restrictions: one on each player's strategic effect and the other on the equilibrium selection mechanism. This observational equivalence transforms the test for collusion / cooperation into a test on structural functions estimated under an equilibrium framework-one that need not be the true model but nonetheless yields informative implications for testing collusive behaviors. In particular, it amounts to a joint test of the strategic effects and the equilibrium selection mechanism. I illustrate the implementation of this test by revisiting the entry game between Wal-Mart and Kmart, as studied by Jia (2008). The estimation results strongly reject the hypothesis that these two chains coordinate their entry decisions to maximize the weighted sum of their profits.