Costly participation and default allocations in all-pay contests

Some important forms of contests have participation costs and `default allocations’ where the contest prize is still awarded even when no-one actively competes. We solve a general, all-pay contest model that allows for flexible forms of these features under arbitrary asymmetry. We then use our framework to better connect the literatures on contests and sales price competition, and use this connection to solve some long-standing problems. Finally, we analyze how participation costs and default allocations can be used as novel, practical tools in contest design. Throughout, the combined presence of participation costs and default allocations often reverse otherwise familiar intuitions.