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Ascending auctions: some impossibility results and their resolutions with final price discounts

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Author Info

  • Laurent Lamy

    (EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics - Ecole d'Économie de Paris, PSE - Paris-Jourdan Sciences Economiques - CNRS : UMR8545 - École des Hautes Études en Sciences Sociales (EHESS) - École des Ponts ParisTech (ENPC) - École normale supérieure [ENS] - Paris)

Abstract

When bidders are not substitutes, we show that there is no standard ascend-ing auction that implements a bidder-optimal competitive equilibrium under truthful bidding. Such an impossibility holds also in environments where the Vickrey payoff vector is a competitive equilibrium payoff and is thus stronger than de Vries, Schummer and Vohra s [On ascending Vickrey auctions for het-erogeneous objects, J. Econ. Theory, 132, 95-118] impossibility result with regards to the Vickrey payoff vector under general valuations. Similarly to Mishra and Parkes [Ascending price Vickrey auctions for general valuations, J. Econ. Theory, 132, 335-366], the impossibility can be circumvented by giving price discounts to the bidders from the final vector of prices. Nevertheless, the similarity is misleading: the solution we propose satisfies a minimality infor-mation revelation property that fails to be satisfied in any ascending auction that implements the Vickrey payoffs for general valuations. We investigate related issues when strictly positive increments have to be used under general continuous valuations.

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Bibliographic Info

Paper provided by HAL in its series PSE Working Papers with number halshs-00575076.

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Date of creation: Dec 2009
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Handle: RePEc:hal:psewpa:halshs-00575076

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Related research

Keywords: ascending auctions ; combinatorial auctions ; bidder-optimal competitive equilibrium ; non-linear pricing ; Vickrey payoffs ; increments;

References

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  1. MISHRA, Debasis & PARKES, David C., 2005. "Ascending price Vickrey auctions for general valuations," CORE Discussion Papers 2005052, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. Paul Milgrom & Robert J. Weber, 1981. "A Theory of Auctions and Competitive Bidding," Discussion Papers 447R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  3. Aytek Erdil & Paul Klemperer, 2010. "A New Payment Rule for Core-Selecting Package Auctions," Journal of the European Economic Association, MIT Press, vol. 8(2-3), pages 537-547, 04-05.
  4. Dubra, Juan & Echenique, Federico & Manelli, Alejandro M., 2009. "English auctions and the Stolper-Samuelson theorem," Journal of Economic Theory, Elsevier, vol. 144(2), pages 825-849, March.
  5. Debasis Mishra & David C. Parkes, 2007. "Multi-item Vickrey-Dutch auctions," Indian Statistical Institute, Planning Unit, New Delhi Discussion Papers 07-04, Indian Statistical Institute, New Delhi, India.
  6. Javier Arin & Elena Inarra, 2001. "Egalitarian solutions in the core," International Journal of Game Theory, Springer, vol. 30(2), pages 187-193.
  7. Jehiel, Philippe & Moldovanu, Benny, 2006. "Allocative and Informational Externalities in Auctions and Related Mechanisms," CEPR Discussion Papers 5558, C.E.P.R. Discussion Papers.
  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. 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.
  10. Bikhchandani, Sushil & Ostroy, Joseph M., 2002. "The Package Assignment Model," Journal of Economic Theory, Elsevier, vol. 107(2), pages 377-406, December.
  11. Claudio Mezzetti, 2004. "Mechanism Design with Interdependent Valuations: Efficiency," Econometrica, Econometric Society, vol. 72(5), pages 1617-1626, 09.
  12. Bikhchandani, Sushil & Ostroy, Joseph M., 2006. "Ascending price Vickrey auctions," Games and Economic Behavior, Elsevier, vol. 55(2), pages 215-241, May.
  13. Laurent Lamy, 2010. "Core-selecting package auctions: a comment on revenue-monotonicity," International Journal of Game Theory, Springer, vol. 39(3), pages 503-510, July.
  14. Dutta, B, 1990. "The Egalitarian Solution and Reduced Game Properties in Convex Games," International Journal of Game Theory, Springer, vol. 19(2), pages 153-69.
  15. Olivier Compte & Philippe Jehiel, 2004. "The Wait-and-See Option in Ascending Price Auctions," Journal of the European Economic Association, MIT Press, vol. 2(2-3), pages 494-503, 04/05.
  16. 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.
  17. Motty Perry & Philip J. Reny, 2002. "An Efficient Auction," Econometrica, Econometric Society, vol. 70(3), pages 1199-1212, May.
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Citations

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Cited by:
  1. Lamy, Laurent, 2012. "On minimal ascending auctions with payment discounts," Games and Economic Behavior, Elsevier, vol. 75(2), pages 990-999.
  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.

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