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Truthful Randomized Mechanisms for Combinatorial Auctions

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  • Shahar Dobzinski

    ()

  • Noam Nisan

    ()

  • Michael Schapira

    ()

Abstract

We design two computationally-efficient incentive-compatible mechanisms for combinatorial auctions with general bidder preferences. Both mechanisms are randomized, and are incentive-compatible in the universal sense. This is in contrast to recent previous work that only addresses the weaker notion of incentive compatibility in expectation. The first mechanism obtains an $O(\sqrt{m})$-approximation of the optimal social welfare for arbitrary bidder valuations -- this is the best approximation possible in polynomial time. The second one obtains an $O(\log^2 m)$-approximation for a subclass of bidder valuations that includes all submodular bidders. This improves over the best previously obtained incentive-compatible mechanism for this class which only provides an $O(\sqrt m)$-approximation.

Suggested Citation

  • Shahar Dobzinski & Noam Nisan & Michael Schapira, 2005. "Truthful Randomized Mechanisms for Combinatorial Auctions," Discussion Paper Series dp408, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
  • Handle: RePEc:huj:dispap:dp408
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    File URL: http://ratio.huji.ac.il/sites/default/files/publications/dp408.pdf
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    References listed on IDEAS

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    1. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401.
    2. Babaioff, Moshe & Feldman, Michal & Nisan, Noam & Winter, Eyal, 2012. "Combinatorial agency," Journal of Economic Theory, Elsevier, vol. 147(3), pages 999-1034.
    3. Liad Blumrosen & Noam Nisan, 2005. "On the Computational Power of Iterative Auctions I: Demand Queries," Discussion Paper Series dp381, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    4. Nisan, Noam & Ronen, Amir, 2001. "Algorithmic Mechanism Design," Games and Economic Behavior, Elsevier, vol. 35(1-2), pages 166-196, April.
    5. 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.
    6. Lehmann, Benny & Lehmann, Daniel & Nisan, Noam, 2006. "Combinatorial auctions with decreasing marginal utilities," Games and Economic Behavior, Elsevier, vol. 55(2), pages 270-296, May.
    7. Mu'alem, Ahuva & Nisan, Noam, 2008. "Truthful approximation mechanisms for restricted combinatorial auctions," Games and Economic Behavior, Elsevier, vol. 64(2), pages 612-631, November.
    8. Groves, Theodore, 1973. "Incentives in Teams," Econometrica, Econometric Society, vol. 41(4), pages 617-631, July.
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    Cited by:

    1. Müller Rudolf & Perea Andrés & Wolf Sascha, 2007. "Combinatorial Scoring Auctions," Research Memorandum 020, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    2. Mu'alem, Ahuva & Nisan, Noam, 2008. "Truthful approximation mechanisms for restricted combinatorial auctions," Games and Economic Behavior, Elsevier, vol. 64(2), pages 612-631, November.

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