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Ascending price Vickrey auctions for general valuations

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  • MISHRA, Debasis
  • PARKES, David C.

Abstract

Ascending price auctions typically involve a single price path with buyers paying their final bid price. Using this traditional definition, no ascending price auction can achieve the Vickrey-Clarke-Groves (VCG) outcome for general private valuations in the combinatorial auction setting. We relax this definition by allowing discounts to buyers from the final price of the auction (or alternatively, calculating the discounts dynamically during the auction) while still maintaining a single price path. Using a notion called universal competitive equilibrium prices, shown to be necessary and sufficient to achieve the VCG outcome using ascending price auctions, we define a broad class of ascending price combinatorial auctions in which truthful bidding by buyers is an ex post Nash equilibrium. Any auction in this class achieves the VCG outcome and ex post efficiency for general valuations. We define two specific auctions in this class by generalizing two known auctions in the literature [11, 24].

Suggested Citation

  • MISHRA, Debasis & PARKES, David C., 2005. "Ascending price Vickrey auctions for general valuations," CORE Discussion Papers 2005052, Universit√© catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  • Handle: RePEc:cor:louvco:2005052
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    References listed on IDEAS

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    1. de Vries, Sven & Schummer, James & Vohra, Rakesh V., 2007. "On ascending Vickrey auctions for heterogeneous objects," Journal of Economic Theory, Elsevier, pages 95-118.
    2. Bikhchandani, Sushil & Ostroy, Joseph M., 2006. "Ascending price Vickrey auctions," Games and Economic Behavior, Elsevier, vol. 55(2), pages 215-241, May.
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    4. Demange, Gabrielle & Gale, David & Sotomayor, Marilda, 1986. "Multi-Item Auctions," Journal of Political Economy, University of Chicago Press, pages 863-872.
    5. Lawrence M. Ausubel & Paul Milgrom, 2004. "Ascending Proxy Auctions," Discussion Papers 03-035, Stanford Institute for Economic Policy Research.
    6. Peter Cramton & Yoav Shoham & Richard Steinberg, 2004. "Combinatorial Auctions," Papers of Peter Cramton 04mit, University of Maryland, Department of Economics - Peter Cramton, revised 2004.
    7. Olivier Compte & Philippe Jehiel, 2007. "Auctions and information acquisition: sealed bid or dynamic formats?," RAND Journal of Economics, RAND Corporation, pages 355-372.
    8. Green, Jerry & Laffont, Jean-Jacques, 1977. "Characterization of Satisfactory Mechanisms for the Revelation of Preferences for Public Goods," Econometrica, Econometric Society, vol. 45(2), pages 427-438, March.
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    10. Peter Cramton & John McMillan & Paul Milgrom & Bradley Miller & Bridger Mitchell & Daniel Vincent & Robert Wilson, 1998. "Simultaneous Ascending Auctions with Package Bidding," Papers of Peter Cramton 98cra2, University of Maryland, Department of Economics - Peter Cramton.
    11. Lawrence M. Ausubel, 2006. "An Efficient Dynamic Auction for Heterogeneous Commodities," American Economic Review, American Economic Association, vol. 96(3), pages 602-629, June.
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    16. Gul, Faruk & Stacchetti, Ennio, 2000. "The English Auction with Differentiated Commodities," Journal of Economic Theory, Elsevier, vol. 92(1), pages 66-95, May.
    17. Michael H. Rothkopf & Aleksandar Pekev{c} & Ronald M. Harstad, 1998. "Computationally Manageable Combinational Auctions," Management Science, INFORMS, vol. 44(8), pages 1131-1147, August.
    18. 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.
    19. S.J. Rassenti & V.L. Smith & R.L. Bulfin, 1982. "A Combinatorial Auction Mechanism for Airport Time Slot Allocation," Bell Journal of Economics, The RAND Corporation, vol. 13(2), pages 402-417, Autumn.
    20. Edward Clarke, 1971. "Multipart pricing of public goods," Public Choice, Springer, vol. 11(1), pages 17-33, September.
    21. Leonard, Herman B, 1983. "Elicitation of Honest Preferences for the Assignment of Individuals to Positions," Journal of Political Economy, University of Chicago Press, vol. 91(3), pages 461-479, June.
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    More about this item

    Keywords

    combinatorial auctions; multi-item auctions; primal-dual algorithm; universal competitive equilibrium; Vickrey auctions;

    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium

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