Multi-item Vickrey-Dutch auctions

Descending price auctions are adopted for goods that must be sold quickly and in private values environments, for instance in flower, fish, and tobacco auctions. In this paper, we introduce ex post efficient descending auctions for two environments: multiple non-identical items and buyers with unit-demand valuations; and multiple identical items and buyers with non-increasing marginal values. Our auctions are designed using the notion of universal competitive equilibrium (UCE) prices and they terminate with UCE prices, from which the Vickrey payments can be determined. For the unit-demand setting, our auction maintains linear and anonymous prices. For the homogeneous items setting, our auction maintains a single price and adopts Ausubel’s notion of “clinching” to compute the final payments dynamically. The auctions support truthful bidding in an ex post Nash equilibrium and terminate with an ex post efficient allocation. In simulation, we illustrate the speed and elicitation advantages of these auctions over their ascending price counterparts. This paper supersedes our two discussion papers titled“A Vickrey-Dutch Clinching Auction”and“MultiItem Vickrey-Dutch Auction for Unit Demand Preferences”. Parkes is supported in part by the National Science Foundation under Grant No. IIS-0331832, an IBM Faculty Award and a Sloan Foundation Fellowship. We thank seminar participants at 2003 Informs annual meeting, Harvard University, Indian Institute of Science, TÜ Berlin Workshop on Combinatorial Auctions, and University of Wisconsin-Madison for their feedback on earlier versions of this work. We also wish to acknowledge the constructive comments of the two anonymous reviewers and associate editor on an earlier version of this paper. Planning Unit, Indian Statistical Institute, New Delhi, India School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA, [email protected]