All-Pay-All Auctions

We consider a class of auctions in which bidders receive (asymmetric) shares of the amount of money raised. Examples include corporate takeovers when potential acquirers have “toeholds” and auctions used to raise money for a public good. We show that the optimal selling mechanism in these cases is a simple “all-pay-all” auction in which all bidders pay a weighted sum of all bids. When bidders receive asymmetric shares of the auction’s revenue, the all-pay-all auction “levels the playing field” and ensures that the bidder with the highest signal receives the object. In other words, the all-pay-all auction is always efficient. These properties contrast sharply with those of standard auction formats such as the first and second price auction, which are not revenue maximizing and generally not efficient when bidders’ shares are asymmetric. Finally, we show that standard auctions may perform particularly poorly when they are used to raise money for a public good. JEL Classification code: D44, C72. Financial support from the Bankard Fund at the University of Virginia is gratefully acknowledged.