On ascending Vickrey auctions for heterogeneous objects

We construct an ascending auction for heterogeneous objects by applying a primal-dual algorithm to a linear program that represents the efficient-allocation problem for this setting. The auction assigns personalized prices to bundles, and asks bidders to report their preferred bundles in each round. A bidder’s prices are increased when he belongs to a “minimally undersupplied” set of bidders. We consider this concept to be the natural generalization of an “overdemanded” set of objects, introduced by Demange et al. (1986) for the one-to-one assignment problem. Under a submodularity condition, the auction implements the Vickrey-Clarke-Groves outcome; we show that this type of condition is somewhat necessary to do so. When classifying the ascending-auction literature in terms of their underlying algorithms, our auction fills a gap in that literature. We relate our results to the recent work of Ausubel and Milgrom (2002).