An E¢ cient Multi-Unit Ascending Auction

We provide an ascending auction that yields an e¢ cient outcome when there are many identical units for sale and bidders have interdependent values and downward-sloping demand. Our ascending auction both extends and generalizes Ausubel’s (1997) and yields the same outcome as Perry and Reny’s (2002) generalization of Vickrey’s (1961) sealed-bid auction. There are two key features of our auction. Bidders are permitted both to express di¤erent demands against di¤erent bidders, as well as to increase their demands. The equilibrium strategies are closely related to the familiar “drop out when price equals value”strategy of the English auction. JEL Classi…cation Number : D44 Keywords: Auctions, Vickrey Auctions, Ascending Auctions. We wish to thank the editor and two anonymous referees who provided detailed and insightful comments leading to the inclusion of substantive new material. We also wish to thank Larry Ausubel for his insights into the FCC spectrum auction and Vijay Krishna for many stimulating discussions concerning ascending auctions, and in particular for an important suggestion regarding the example in Section 3. Both authors gratefully acknowledge …nancial support from the National Science Foundation (SES-9905599, SES-0214421, and SES-0001744).