The optimal sorting of players in contests between groups

We study how aggregate effort exerted in contests between groups of heterogeneous players depends on the sorting of players into groups. We show that the optimal sorting depends on the curvature of the effort cost function. From the perspective of a contest organizer whose objective is to maximize aggregate effort, it is optimal to sort players in a way that minimizes the variation in ability across groups if the effort cost function is moderately steep. However, for a sufficiently steep effort cost function, the optimal sorting of players may be the one that maximizes the variation in ability across groups.