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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].

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Bibliographic Info

Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 2005052.

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Date of creation: 00 Aug 2005
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Handle: RePEc:cor:louvco:2005052

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

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References

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  1. Philippe Jehiel & Moritz Meyer-ter-Vehn & Benny Moldovanu & William R. Zame, 2005. "The Limits of Ex-Post Implementation," UCLA Economics Working Papers 839, UCLA Department of Economics.
  2. Edward Clarke, 1971. "Multipart pricing of public goods," Public Choice, Springer, vol. 11(1), pages 17-33, September.
  3. Bikhchandani, Sushil & Ostroy, Joseph M., 2002. "The Package Assignment Model," Journal of Economic Theory, Elsevier, vol. 107(2), pages 377-406, December.
  4. Groves, Theodore, 1973. "Incentives in Teams," Econometrica, Econometric Society, vol. 41(4), pages 617-31, July.
  5. Lawrence M. Ausubel & Paul Milgrom, 2002. "Ascending Auctions with Package Bidding," Working Papers 02004, Stanford University, Department of Economics.
  6. Gul, Faruk & Stacchetti, Ennio, 2000. "The English Auction with Differentiated Commodities," Journal of Economic Theory, Elsevier, vol. 92(1), pages 66-95, May.
  7. 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.
  8. Peter Cramton & Yoav Shoham & Richard Steinberg, 2004. "Combinatorial Auctions," Papers of Peter Cramton 04mit, University of Maryland, Department of Economics - Peter Cramton, revised 2004.
  9. Peter Cramton, 1998. "Ascending Auctions," Papers of Peter Cramton 98eer, University of Maryland, Department of Economics - Peter Cramton, revised 28 Jul 1998.
  10. Olivier Compte & Philippe Jehiel, 2005. "Auctions and Information acquisition: Sealed-bid or Dynamic Formats?," Levine's Bibliography 784828000000000495, UCLA Department of Economics.
  11. de Vries, Sven & Schummer, James & Vohra, Rakesh V., 2007. "On ascending Vickrey auctions for heterogeneous objects," Journal of Economic Theory, Elsevier, vol. 132(1), pages 95-118, January.
  12. William Vickrey, 1961. "Counterspeculation, Auctions, And Competitive Sealed Tenders," Journal of Finance, American Finance Association, vol. 16(1), pages 8-37, 03.
  13. Bikhchandani, Sushil & Ostroy, Joseph M., 2006. "Ascending price Vickrey auctions," Games and Economic Behavior, Elsevier, vol. 55(2), pages 215-241, May.
  14. 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 461-79, June.
  15. Lawrence M. Ausubel, 2004. "An Efficient Ascending-Bid Auction for Multiple Objects," American Economic Review, American Economic Association, vol. 94(5), pages 1452-1475, December.
  16. Lawrence M. Ausubel & Paul Milgrom, 2004. "Ascending Proxy Auctions," Discussion Papers 03-035, Stanford Institute for Economic Policy Research.
  17. 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 427-38, March.
  18. Demange, Gabrielle & Gale, David & Sotomayor, Marilda, 1986. "Multi-Item Auctions," Journal of Political Economy, University of Chicago Press, vol. 94(4), pages 863-72, August.
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Citations

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Cited by:
  1. Andersson, Tommy & Andersson, Christer & Andersson, Ola, 2010. "Sealed Bid Auctions vs. Ascending Bid Auctions: An Experimental Study," Working Papers 2010:17, Lund University, Department of Economics.
  2. Hitoshi Matsushima, 2011. "Price-Based Combinatorial Auction: Connectedness and Representative Valuations," CIRJE F-Series CIRJE-F-806, CIRJE, Faculty of Economics, University of Tokyo.
  3. repec:hal:wpaper:halshs-00575076 is not listed on IDEAS
  4. Laurent Lamy, 2007. "Contingent Auctions with Allocative Externalities: Vickrey vs. the Ausubel-Milgrom Proxy Auction," 2007 Meeting Papers 427, Society for Economic Dynamics.
  5. Lavi, Ron & Oren, Sigal, 2012. "Side-communication yields efficiency of ascending auctions: The two-items case," Games and Economic Behavior, Elsevier, vol. 76(2), pages 439-456.
  6. 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.
  7. Akiyoshi Shioura & Zaifu Yang, 2013. "Equilibrium, Auction, Multiple Substitutes and Complements," Discussion Papers 13/17, Department of Economics, University of York.
  8. Andersson, Tommy & Erlanson, Albin, 2012. "Multi-Item Vickery-English-Dutch Auctions," Working Papers 2012:17, Lund University, Department of Economics, revised 15 Jan 2013.
  9. Lamy, Laurent, 2012. "On minimal ascending auctions with payment discounts," Games and Economic Behavior, Elsevier, vol. 75(2), pages 990-999.
  10. Laurent Lamy, 2009. "Ascending auctions: some impossibility results and their resolutions with final price discounts," PSE Working Papers halshs-00575076, HAL.
  11. 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.
  12. Sano, Ryuji, 2011. "Incentives in core-selecting auctions with single-minded bidders," Games and Economic Behavior, Elsevier, vol. 72(2), pages 602-606, June.
  13. Mochon, A. & Saez, Y. & Gomez-Barroso, J.L. & Isasi, P., 2012. "Exploring pricing rules in combinatorial sealed-bid auctions," Journal of Economic Behavior & Organization, Elsevier, vol. 82(2), pages 462-478.
  14. Christer Andersson & Ola Andersson & Tommy Andersson, 2013. "Sealed bid auctions versus ascending bid auctions: an experimental study," Review of Economic Design, Springer, vol. 17(1), pages 1-16, March.

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