Contests with ties

We study two-player all-pay contests in which there is a positive probability of a tied outcome. We show that the players' efforts in equilibrium do not depend on the expected prize in the case of a tie given that this prize is smaller than the prize for winning. The implications of this result are twofold. First, in symmetric one-stage contests, the designer who wishes to maximize the expected total effort should not award a prize in the case of a tie which is larger than one-third of the prize for winning. Second, in multi-stage contests, the designer should not limit the number of stages (tie-breaks) but should allow the contest to continue until a winner is decided.