Testing collusion and cooperation in binary choice games

This paper studies the testable implication of players' collusive or cooperative behaviours in a binary choice game with complete information. In this paper, these behaviours are defined as players coordinating their actions to maximize the weighted sum of their payoffs. I show that this collusive model is observationally equivalent to an equilibrium model that imposes two restrictions. The first restriction is on each player's strategic effect and the second one requires a particular equilibrium selection mechanism. Under the equilibrium condition, these joint restrictions are simple to test using tools in the literature on empirical games. This test, as suggested by the observational equivalence result, is the same as testing collusive and cooperative behaviours. I illustrate the implementation of this test by revisiting the entry game between Walmart and Kmart studied by Jia (2008). Under the equilibrium condition, Jia's original estimates are consistent with the first restriction on the strategic effects, serving as a warning sign of potential collusion. This paper tests and rejects the second restriction on the equilibrium selection mechanism. Thus, the empirical evidence suggests that Walmart and Kmart did not collude on their entry decisions.