nonparametric test for cooperation in discrete games.

This article develops a nonparametric test for detecting cooperative (coalitional) behavior among players in discrete, static games, defined as players maximizing an unknown joint objective function symmetric in players' pay-offs when matched on observable characteristics. Under exchangeability and symmetry assumptions on pay-offs conditional on matched covariates, cooperation implies that the probability of observing any outcome in a certain class must equal the probability of observing any permutation of that outcome. The authors construct a kernel-based U-statistic test based on these conditional moment equalities, establish its asymptotic normality under the null of cooperation, and demonstrate consistency against noncooperative alternatives. Monte Carlo experiments illustrate the test's size and power properties in binary choice games, showing sensitivity to equilibrium selection mechanisms and strategic asymmetries. An empirical application to expansion decisions by Lowe's and Home Depot across U.S. markets finds evidence consistent with cooperation in smaller markets but rejects cooperation in larger ones, using store presence and distribution center distance as matching covariates.