Non - Parametric Tests of the Tragedy

Drawing on recent results in the industrial organization literature (Carvajal et al. 2013), we derive non-parametric tests of the tragedy of the commons. Our approach allows group output to be any arbitrarily concave, differentiable function of total inputs and for individual exploiters of the resource to have any arbitrary convex, differentiable cost of supplying inputs. We show that observed group output and individual inputs are consistent with the tragedy of the commons only if the data follow certain patterns denoted as the common-ratio property and the co-monotone property. Our basic results for a static average-return game can be extended to tragedies with consistent conjecture (as opposed to Nash) equilibria, to dynamic resources, and to the averagecost game. JEL Codes: C14, C72, D21, D23, Q2, Q3