Ascending Price Vickrey Auctions
by
Sushil Bikhchandani
UCLA

An ascending price auction for a single object is (1) a dynamic mechanism for discovering the smallest price at which demand equals supply; (2) it gives each bidder his marginal product, therefore ensuring that it is incentive compatible to bid truthfully; moreover, (3) it is also an example of a primal-dual algorithm in linear programming. An ascending price auction for the assignment model (with several heterogeneous objects, but each buyer wishes to purchase at most one) has the same properties. We show that (1)-(3) hold for ascending price auctions for multiple units of homogeneous objects (where buyers may purchase more than one unit). The multiplicity of units purchased by buyers introduces an important qualification: unlike the single object model and the assignment model where there is one price for each commodity, in the multi-unit auction prices must be non-linear and non-anonymous for equilibrium to exist and be efficient. Thus, the price of a package to a buyer may not be the sum of the prices of the single objects, and different buyers may face different prices for the same package. We demonstrate that the ascending price auction proposed by Ausubel (i) raises prices for packages until they reach their smallest market clearing prices; (ii) at these prices bidders get their marginal products; (iii) the auction is a primal-dual algorithm applied to an appropriate linear programming formulation. The solution of the dual of this linear program yields market clearing prices. Our results demonstrate the similarity between ascending price auctions for the single object and the multi-unit models. We plan to investigate whether the similarity extends to ascending price auctions of multiple heterogeneous objects.

Date received: April 22, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caez-29.