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Truthful approximation mechanisms for restricted combinatorial auctions

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  • Mu'alem, Ahuva
  • Nisan, Noam

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.

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Bibliographic Info

Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 64 (2008)
Issue (Month): 2 (November)
Pages: 612-631

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Handle: RePEc:eee:gamebe:v:64:y:2008:i:2:p:612-631

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Web page: http://www.elsevier.com/locate/inca/622836

Related research

Keywords: Mechanism design Combinatorial auctions Multi-unit auctions Multi-unit combinatorial auctions Approximation algorithms;

References

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  1. Nisan, Noam & Ronen, Amir, 2001. "Algorithmic Mechanism Design," Games and Economic Behavior, Elsevier, vol. 35(1-2), pages 166-196, April.
  2. William Vickrey, 1961. "Counterspeculation, Auctions, And Competitive Sealed Tenders," Journal of Finance, American Finance Association, vol. 16(1), pages 8-37, 03.
  3. Holzman, Ron & Kfir-Dahav, Noa & Monderer, Dov & Tennenholtz, Moshe, 2004. "Bundling equilibrium in combinatorial auctions," Games and Economic Behavior, Elsevier, vol. 47(1), pages 104-123, April.
  4. Edward Clarke, 1971. "Multipart pricing of public goods," Public Choice, Springer, vol. 11(1), pages 17-33, September.
  5. Caprara, Alberto & Kellerer, Hans & Pferschy, Ulrich & Pisinger, David, 2000. "Approximation algorithms for knapsack problems with cardinality constraints," European Journal of Operational Research, Elsevier, vol. 123(2), pages 333-345, June.
  6. Nisan, Noam & Segal, Ilya, 2006. "The communication requirements of efficient allocations and supporting prices," Journal of Economic Theory, Elsevier, vol. 129(1), pages 192-224, July.
  7. Tuomas Sandholm & Subhash Suri & Andrew Gilpin & David Levine, 2005. "CABOB: A Fast Optimal Algorithm for Winner Determination in Combinatorial Auctions," Management Science, INFORMS, vol. 51(3), pages 374-390, March.
  8. Shahar Dobzinski & Noam Nisan & Michael Schapira, 2005. "Truthful Randomized Mechanisms for Combinatorial Auctions," Discussion Paper Series dp408, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  9. Liad Blumrosen & Noam Nisan, 2005. "On the Computational Power of Iterative Auctions II: Ascending Auctions," Discussion Paper Series dp382, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  10. Groves, Theodore, 1973. "Incentives in Teams," Econometrica, Econometric Society, vol. 41(4), pages 617-31, July.
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Cited by:
  1. Sano, Ryuji, 2011. "Incentives in core-selecting auctions with single-minded bidders," Games and Economic Behavior, Elsevier, vol. 72(2), pages 602-606, June.
  2. Babaioff, Moshe & Blumrosen, Liad, 2008. "Computationally-feasible truthful auctions for convex bundles," Games and Economic Behavior, Elsevier, vol. 63(2), pages 588-620, July.

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