Abstract
We study two all-pay auctions, where contestants cannot compete in both auctions. One contest has a higher prize than the other. Ideally, high-ability contestants should participate in the contest with a higher prize. We find that this is not necessarily the case. We show that the top contestant may choose to participate in the contest with a lower prize. In a subgame perfect mixed-strategy equilibrium, the probability that the most able contestant will choose to participate in the inferior contest is more than 50%, under certain conditions.
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