Auctions with Options for Re-auction

Abstract

A seller has one unit to sell using an English auction mechanism similar to internet auction markets, such as eBay. Bidders appear according to a random arrival process. The seller chooses a reserve price and duration for each auction. If the reserve is not met, the seller passes in the object and conducts another auction with a new, randomly chosen, set of bidders. We distinguish reserves that embody an institutional commitment not to sell below that price, from those that do not. In each case, we find the optimal reserve price and the optimal auction duration. Without price commitment, the equilibrium reserve is too low for allocative efficiency, whereas the optimal reserve with commitment is shown to be too high when the distribution of bidder valuations exhibits an increasing hazard rate. It might even be socially preferable to allow reserve price commitments. With respect to duration, a version of the Diamond paradox afflicts sellers who cannot commit to price; auctions facilitate valuable duration commitments that increase buyer competition and raise expected revenue. With commitment, price posting (equivalent to a zero-length auction) is the dominant selling mechanism.