An Ascending Vickrey Auction for Selling Bases of a Matroid

Authors:
Sushil Bikhchandani;Sven de Vries;James Schummer;Rakesh V. Vohra
Affiliations:
Anderson Graduate School of Management, University of California, Los Angeles, Los Angeles, California 90095;FB IV--Mathematik, Universität Trier, 54286 Trier, Germany;Department of Managerial Economics and Decision Sciences, Kellogg School of Management, Northwestern University, Evanston, Illinois 60208;Department of Managerial Economics and Decision Sciences, Kellogg School of Management, Northwestern University, Evanston, Illinois 60208
Venue:
Operations Research
Year:
2011

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Abstract

Consider selling bundles of indivisible goods to buyers with concave utilities that are additively separable in money and goods. We propose an ascending auction for the case when the seller is constrained to sell bundles whose elements form a basis of a matroid. It extends easily to polymatroids. Applications include scheduling, allocation of homogeneous goods, and spatially distributed markets, among others. Our ascending auction induces buyers to bid truthfully and returns the economically efficient basis. Unlike other ascending auctions for this environment, ours runs in pseudopolynomial or polynomial time. Furthermore, we prove the impossibility of an ascending auction for nonmatroidal independence set-systems.