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On the Computational Power of Iterative Auctions I: Demand Queries

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  • Liad Blumrosen
  • Noam Nisan

Abstract

We study the computational power and limitations of iterative combinatorial auctions. Most existing iterative combinatorial auctions are based on repeatedly suggesting prices for bundles of items, and querying the bidders for their ``demand'' under these prices. We prove several results regarding such auctions that use a polynomial number of demand queries: (1) that such auctions can simulate several other natural types of queries; (2) that such auctions can solve linear programming relaxations of winner determination problems; (3) that they can approximate the optimal allocation as well as generally possible using polynomial communication or computation, while weaker types of queries can not do so. We also initiate the study of how can the prices of bundles be represented when they are not linear, and show that the ``default'' representation has severe limitations.

Suggested Citation

  • 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.
  • Handle: RePEc:huj:dispap:dp381
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    References listed on IDEAS

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    1. Babaioff, Moshe & Feldman, Michal & Nisan, Noam & Winter, Eyal, 2012. "Combinatorial agency," Journal of Economic Theory, Elsevier, vol. 147(3), pages 999-1034.
    2. Ausubel Lawrence M & Milgrom Paul R, 2002. "Ascending Auctions with Package Bidding," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 1(1), pages 1-44, August.
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    5. 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.
    6. Demange, Gabrielle & Gale, David & Sotomayor, Marilda, 1986. "Multi-Item Auctions," Journal of Political Economy, University of Chicago Press, vol. 94(4), pages 863-872, August.
    7. Peter Cramton & Yoav Shoham & Richard Steinberg, 2004. "Combinatorial Auctions," Papers of Peter Cramton 04mit, University of Maryland, Department of Economics - Peter Cramton, revised 2004.
    8. Liad Blumrosen & Noam Nisan, 2005. "On the Computational Power of Iterative Auctions II: Ascending Auctions," Discussion Paper Series dp382, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    9. 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.
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    Cited by:

    1. Kagel, John H. & Lien, Yuanchuan & Milgrom, Paul, 2014. "Ascending prices and package bidding: Further experimental analysis," Games and Economic Behavior, Elsevier, vol. 85(C), pages 210-231.
    2. Liad Blumrosen & Noam Nisan, 2005. "On the Computational Power of Iterative Auctions II: Ascending Auctions," Discussion Paper Series dp382, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    3. 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.
    4. Shahar Dobzinski & Noam Nisan & Michael Schapira, 2010. "Approximation Algorithms for Combinatorial Auctions with Complement-Free Bidders," Mathematics of Operations Research, INFORMS, vol. 35(1), pages 1-13, February.
    5. Schneider, S. & Shabalin, P. & Bichler, M., 2010. "On the robustness of non-linear personalized price combinatorial auctions," European Journal of Operational Research, Elsevier, vol. 206(1), pages 248-259, October.
    6. Ben-Zwi, Oren, 2017. "Walrasian's characterization and a universal ascending auction," Games and Economic Behavior, Elsevier, vol. 104(C), pages 456-467.
    7. John H. Kagel & Yuanchuan Lien & Paul Milgrom, 2010. "Ascending Prices and Package Bidding: A Theoretical and Experimental Analysis," American Economic Journal: Microeconomics, American Economic Association, vol. 2(3), pages 160-185, August.

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    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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