DP7224 Best-of-Three All-Pay Auctions
We study a three-stage all-pay auction with two players in which the first player to win two matches wins the best-of-three all-pay auction. The players have values of winning the contest and may have also values of losing, the latter depending on the stage in which the contest is decided. It is shown that without values of losing, if players are heterogenous (they have different values) the best-of-three all-pay auction is less competitive (the difference between the players' probabilities to win is larger) as well as less productive (the players' total expected effort is smaller) than the one-stage all-pay auction. If players are homogenous, however, the productivity and obviously the competitiveness of the best-of-three all-pay auction and the one-stage all-pay auction are identical. These results hold even if players have values of losing that do not depend on the stage in which the contest is decided. However, the best-of-three all-pay auction with different values of losing over the contest's stages may be more productive than the one-stage all-pay auction.