A nonparametric test for cooperation in discrete games

Abstract

Summary We propose a nonparametric test for cooperative behaviour among players in discrete, static games. Assuming that certain exchangeability conditions hold if we match observable characteristics across all players, we obtain testable implications for cooperative (coalitional) behaviour, which we define as occurring when players maximise an unknown joint objective function that is symmetric conditional on the matching. Cooperation implies the existence of a class of outcomes $\mathcal {Y}$ such that, conditional on the matching, the probability of observing an outcome $y\in \mathcal {Y}$ must be equal to the probability of observing any permutation of y. We present a nonparametric econometric test and we characterise its asymptotic properties. We apply our test to expansion/entry decisions of Lowe’s and Home Depot in the contiguous United States and we find that, while outcomes are consistent with noncooperative behaviour in larger markets, we fail to reject cooperation in smaller markets.