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Price-Based Combinatorial Auction: Connectedness and Representative Valuations

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  • Hitoshi Matsushima

    (Faculty of Economics, University of Tokyo)

Abstract

We investigate combinatorial auctions from a practical perspective. The auctioneer gathers information according to a dynamical protocol termed ask price procedure. We demonstrate a method for elucidating whether a procedure gathers sufficient information for deriving a VCG mechanism. We calculate representative valuation functions in a history-contingent manner, and show that it is necessary and sufficient to examine whether efficient allocations with and without any buyer associated with the profile of representative valuation functions were revealed. This method is tractable, and can be applied to general procedures with connectedness. The representative valuation functions could be the sufficient statistics for privacy preservation.

Suggested Citation

  • Hitoshi Matsushima, 2011. "Price-Based Combinatorial Auction: Connectedness and Representative Valuations," CARF F-Series CARF-F-261, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    • Handle: RePEc:cfi:fseres:cf261
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    References listed on IDEAS

    as
    1. Hitoshi Matsushima, 2010. "Price-Based Combinatorial Auction Design: Representative Valuations," KIER Working Papers 742, Kyoto University, Institute of Economic Research.
    2. Milgrom,Paul, 2004. "Putting Auction Theory to Work," Cambridge Books, Cambridge University Press, number 9780521536721.
    3. William Vickrey, 1961. "Counterspeculation, Auctions, And Competitive Sealed Tenders," Journal of Finance, American Finance Association, vol. 16(1), pages 8-37, March.
    4. Myerson, Roger B, 1979. "Incentive Compatibility and the Bargaining Problem," Econometrica, Econometric Society, vol. 47(1), pages 61-73, January.
    5. Lawrence M. Ausubel, 2006. "An Efficient Dynamic Auction for Heterogeneous Commodities," American Economic Review, American Economic Association, vol. 96(3), pages 602-629, June.
    6. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    7. Bikhchandani, Sushil & Ostroy, Joseph M., 2002. "The Package Assignment Model," Journal of Economic Theory, Elsevier, vol. 107(2), pages 377-406, December.
    8. Mishra, Debasis & Parkes, David C., 2007. "Ascending price Vickrey auctions for general valuations," Journal of Economic Theory, Elsevier, vol. 132(1), pages 335-366, January.
    9. Kelso, Alexander S, Jr & Crawford, Vincent P, 1982. "Job Matching, Coalition Formation, and Gross Substitutes," Econometrica, Econometric Society, vol. 50(6), pages 1483-1504, November.
    10. 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.
    11. Jean Tirole, 1999. "Incomplete Contracts: Where Do We Stand?," Econometrica, Econometric Society, vol. 67(4), pages 741-782, July.
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    Cited by:

    1. Matsushima Hitoshi, 2018. "Connected Price Dynamics with Revealed Preferences and Auctioneer’s Discretion in VCG Combinatorial Auction," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 18(1), pages 1-16, January.
    2. Hitoshi Matsushima, 2010. "Auctioneer's Discretion in Combinatorial Auctions," CARF F-Series CARF-F-293, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Sep 2012.

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