All-Pay Contests with Costly Participation and Default Allocations

Abstract

Players often face direct costs of participating in contests due to set-up costs or minimum outlays. In such cases, the outcome can depend upon the `default allocation' - how the prize is awarded if no player actively competes. The existing literature has neglected this issue by implicitly assuming that the prize is only awarded under active participation. However, in practice, there are many important situations where this does not apply - policymakers still allocate funding even when there are no lobbying activities, and employees still gain new responsibilities even when no-one competed for them. To help better address these issues, our paper makes three main contributions. First, it provides a general framework that can explicitly characterize all potential equilibria in all-pay contests (e.g. Siegel 2009) while allowing for any default allocation, any form of participation cost, and any arbitrary level of asymmetry. Second, as a by-product, the paper formally connects all-pay contests to the family of 'clearinghouse' sales models (e.g. Baye and Morgan 2001) and shows, for the first time, how they can be solved for any arbitrary asymmetry. Third, to further demonstrate our framework's power, the paper shows how default allocations can be used as a new tool in optimal contest design. Joint work with Chris Wilson