Costly Participation and Default Allocations in All-Pay Contests

Some important contests have participation costs and `default allocations’ where the contest prize is still awarded even when no-one actively competes. This paper incorporates flexible forms of these features into a general (single-prize) all-pay contest model under arbitrary asymmetry. We offer a tractable equilibrium characterization that fundamentally rests on only two measures (per-player): `reach' and a new concept, `strength'. We then i) analyze how participation costs and default allocations can be employed as novel tools in contest design, ii) solve `clearinghouse' models of price competition under full asymmetry for the first time, and iii) offer a new equilibrium refinement for symmetric multi-player all-pay contests. Throughout, the combination of participation costs and default allocations is key and often reverses otherwise familiar intuitions.