All‐Pay Auctions With A Buy‐Price Option

This paper studies all‐pay auctions in which there is a buy‐price option for bidders to guarantee purchases at a seller‐specified price. We analyze symmetric increasing bidding equilibria in the first‐ and second‐price all‐pay auctions with the buy‐price option. While the optimal buy‐price in the second price is higher than are those in the first‐price all‐pay auction, both formats maintain the same expected profit. With an endogenous entry process, all‐pay auctions with the buy‐price can attract more consumers and ultimately reach a higher expected profit than does the uniform posted‐price selling mechanism. (JEL D44, L11, L81)