The lowest-bid all-pay-auction as a fund-raising mechanism: Theoretically optimal but behaviorally fragile

We study the optimal design of mechanisms for the private provision of public goods in a simplesetting in which donors compete for a prize of commonly known value. The optimal mechanism in thismodel is the lowest-price all-pay auction – a mechanism in which the highest bidder wins but allbidders pay the lowest bid. The highest amount for the public good is generated in the unique,symmetric, mixed-strategy equilibrium of this mechanism. We derive the equilibrium distributionfunction in a closed form for any number of bidders. We then compare various all-pay auctions andlotteries in lieu of voluntary contributions with a battery of laboratory experiments. Theperformance of the optimal mechanism depends on the level of competition. The lowest-price all-payauction dominates the remaining auction formats with three competing bidders, but is inferior tothe own-pay auction and the lottery with only two bidders.