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 as well as 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 heterogeneous the best-of-three all-pay auction is less productive than the one-stage all-pay auction. ► 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.