Auctions with Endogenous Quantity

Abstract

This article studies auctions in which several sellers compete for the right to sell to a market characterized by a negatively sloped demand curve. In this environment the quantity traded becomes endogenous; this effect leads to three results concerning the outcomes of open versus (first-price) sealed-bid auctions. First, an open auction yields a higher expected price than does sealed bidding. Second, and more important, the open auction captures less of the potential gains from trade than does the sealed-bid auction. Third, for broad classes of demand curves, the efficiency gains from switching to sealed bids from an open auction accrue to both sellers and the buyer, so that all concerned parties would agree to the change. A direct application of the theory is to procurement, the heavy use of sealed bidding in procurement is seen as rational in light of these results. Auction models with endogenous quantity could be an alternative to price-setting oligopoly models for the study of price formation in general, for the latter impose strong information requirements on agents and yield only equilibrium price vectors, not equilibrium processes for determining prices.