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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

Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 132 (2007)
Issue (Month): 1 (January)
Pages: 335-366

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Handle: RePEc:eee:jetheo:v:132:y:2007:i:1:p:335-366

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Web page: http://www.elsevier.com/locate/inca/622869

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References

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  1. Philippe Jehiel & Moritz Meyer-ter-Vehn & Benny Moldovanu & William R. Zame, 2006. "The Limits of ex post Implementation," Econometrica, Econometric Society, vol. 74(3), pages 585-610, 05.
  2. 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.
  3. Groves, Theodore, 1973. "Incentives in Teams," Econometrica, Econometric Society, vol. 41(4), pages 617-31, July.
  4. 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.
  5. Lawrence M. Ausubel & Paul Milgrom, 2002. "Ascending Auctions with Package Bidding," Working Papers 02004, Stanford University, Department of Economics.
  6. 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.
  7. 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.
  8. Olivier Compte & Philippe Jehiel, 2007. "Auctions and information acquisition: sealed bid or dynamic formats?," RAND Journal of Economics, RAND Corporation, vol. 38(2), pages 355-372, 06.
  9. Peter Cramton, 1998. "Ascending Auctions," Papers of Peter Cramton 98eer, University of Maryland, Department of Economics - Peter Cramton, revised 28 Jul 1998.
  10. Lawrence M. Ausubel & Paul Milgrom, 2004. "Ascending Proxy Auctions," Discussion Papers 03-035, Stanford Institute for Economic Policy Research.
  11. 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.
  12. Gul, Faruk & Stacchetti, Ennio, 2000. "The English Auction with Differentiated Commodities," Journal of Economic Theory, Elsevier, vol. 92(1), pages 66-95, May.
  13. 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.
  14. Bikhchandani, Sushil & Ostroy, Joseph M., 2002. "The Package Assignment Model," Journal of Economic Theory, Elsevier, vol. 107(2), pages 377-406, December.
  15. Edward Clarke, 1971. "Multipart pricing of public goods," Public Choice, Springer, vol. 11(1), pages 17-33, September.
  16. Bikhchandani, Sushil & Ostroy, Joseph M., 2006. "Ascending price Vickrey auctions," Games and Economic Behavior, Elsevier, vol. 55(2), pages 215-241, May.
  17. William Vickrey, 1961. "Counterspeculation, Auctions, And Competitive Sealed Tenders," Journal of Finance, American Finance Association, vol. 16(1), pages 8-37, 03.
  18. Peter Cramton & Yoav Shoham & Richard Steinberg, 2004. "Combinatorial Auctions," Papers of Peter Cramton 04mit, University of Maryland, Department of Economics - Peter Cramton, revised 2004.
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Citations

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Cited by:
  1. Laurent Lamy, 2007. "Contingent Auctions with Allocative Externalities: Vickrey vs. the Ausubel-Milgrom Proxy Auction," 2007 Meeting Papers 427, Society for Economic Dynamics.
  2. 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.
  3. 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.
  4. 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.
  5. Laurent Lamy, 2009. "Ascending auctions: some impossibility results and their resolutions with final price discounts," PSE Working Papers halshs-00575076, HAL.
  6. 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.
  7. Sano, Ryuji, 2011. "Incentives in core-selecting auctions with single-minded bidders," Games and Economic Behavior, Elsevier, vol. 72(2), pages 602-606, June.
  8. Hitoshi Matsushima, 2011. "Price-Based Combinatorial Auction: Connectedness and Representative Valuations," CIRJE F-Series CIRJE-F-806, CIRJE, Faculty of Economics, University of Tokyo.
  9. Shuhei Morimoto & Shigehiro Serizawa, 2012. "Strategy-proofness and Efficiency with Nonquasi-linear Preferences: A Characterization of Minimum Price Walrasian Rule," ISER Discussion Paper 0852, Institute of Social and Economic Research, Osaka University.
  10. Andersson, Tommy & Erlanson, Albin, 2012. "Multi-Item Vickery-English-Dutch Auctions," Working Papers 2012:17, Lund University, Department of Economics, revised 15 Jan 2013.
  11. repec:hal:wpaper:halshs-00575076 is not listed on IDEAS
  12. 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.
  13. Lamy, Laurent, 2012. "On minimal ascending auctions with payment discounts," Games and Economic Behavior, Elsevier, vol. 75(2), pages 990-999.
  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.
  15. Akiyoshi Shioura & Zaifu Yang, 2013. "Equilibrium, Auction, Multiple Substitutes and Complements," Discussion Papers 13/17, Department of Economics, University of York.

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