On the optimal allocation of prizes in best-of-three all-pay auctions

We study best-of-three all-pay auctions with two players who compete in three stages with a single match per stage. The first player to win two matches wins the contest. We assume that a prize sum is given, and show that if players are symmetric, the allocation of prizes does not have any effect on the players’ expected total effort. On the other hand, if players are asymmetric, in order to maximize the players’ expected total effort, independent of the players’ types, it is not optimal to allocate a single final prize to the winner. Instead, it is optimal to allocate intermediate prizes in the first stage or/and in the second stage in addition to the final prize. When the asymmetry of the players’ types is sufficiently high, it is optimal to allocate intermediate prizes in both two first stages and a final prize to the winner.