Auctions with Endogenous Quantity
研究多个卖家竞争向需求曲线向下倾斜的市场销售时，交易数量内生决定对拍卖结果的影响，发现公开拍卖比密封投标价格更高但效率更低，且密封投标能带来帕累托改进。
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.