Selling without Reserve as the Content of Optimal Auctions∗

Potential bidders respond to a seller’s choice of auction mechanism for a common-value or affiliated-values asset by endogenous decisions whether to incur a participation cost (and observe a private signal), or forego competing. Privately informed participants decide whether to incur a bid-preparation cost and pay an entry fee, or cease competing. The resulting revenue identity for any auction mechanism implies that optimal auctions are allocatively efficient; a nontrivial reserve price is revenue-inferior for any common-value auction. The set of optimal auctions is otherwise contentless, in that any auction that sells without reserve is within the setting of one continuous parameter of an optimal auction; seller’s surplus-extracting tools are now substitutes, not complements. Revenue comparisons from the exogenous-bidders literature are upheld in a half-space of parameters, overturned in a half-space. Many econometric studies of auction markets are seen to be flawed in their identification of the number of bidders. ∗I thank the Fuqua School of Business at Duke Univeristy and the Olin School of Business at Washington University for their hospitality during the writing of this paper. Special thanks to Octavian Carare for several iteratons of assistance with three-dimensional diagrams.