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Published November 2008 | Accepted Version
Journal Article Open

Truthful approximation mechanisms for restricted combinatorial auctions

Abstract

When attempting to design a truthful mechanism for a computationally hard problem such as combinatorial auctions, one is faced with the problem that most efficiently computable heuristics can not be embedded in any truthful mechanism (e.g. VCG-like payment rules will not ensure truthfulness). We develop a set of techniques that allow constructing efficiently computable truthful mechanisms for combinatorial auctions in the special case where each bidder desires a specific known subset of items and only the valuation is unknown by the mechanism (the single parameter case). For this case we extend the work of Lehmann, O'Callaghan, and Shoham, who presented greedy heuristics. We show how to use If-Then-Else constructs, perform a partial search, and use the LP relaxation. We apply these techniques for several canonical types of combinatorial auctions, obtaining truthful mechanisms with provable approximation ratios.

Additional Information

Copyright © 2008 Elsevier Inc. Received 20 April 2006. Published November 2008. Available online 29 February 2008. We thank Daniel Lehmann, Ron Lavi, Shahar Dobzinski, and Liad Blumrosen for helpful comments and Gil Kalai for an early discussion. Special Issue in Honor of Michael B. Maschler, Games and Economic Behavior Volume 64, Issue 2, November 2008.

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August 22, 2023
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October 17, 2023