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Fraction auctions: The tradeoff between efficiency and running time

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  • Grigorieva, Elena
  • Jean-Jacques Herings, P.
  • Müller, Rudolf
  • Vermeulen, Dries

Abstract

This paper studies the sales of a single indivisible object where bidders have continuous valuations. In Grigorieva et al. [14] it was shown that, in this setting, query auctions necessarily allocate inefficiently in equilibrium. In this paper we propose a new sequential auction, called the c-fraction auction. We show the existence of an ex-post equilibrium, called bluff equilibrium, in which bidders behave truthfully except for particular constellations of observed bids at which it is optimal to pretend a slightly higher valuation. We show c-fraction auctions guarantee approximate efficiency at any desired level of accuracy, independent of the number of bidders, when bidders choose to play the bluff equilibrium. We discuss the running time and the efficiency in the bluff equilibrium. We show that by changing the parameter c of the auction we can trade off efficiency against running time.

Suggested Citation

  • Grigorieva, Elena & Jean-Jacques Herings, P. & Müller, Rudolf & Vermeulen, Dries, 2012. "Fraction auctions: The tradeoff between efficiency and running time," European Journal of Operational Research, Elsevier, vol. 220(2), pages 577-587.
    • Handle: RePEc:eee:ejores:v:220:y:2012:i:2:p:577-587
    DOI: 10.1016/j.ejor.2012.01.063
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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, vol. 132(1), pages 95-118, January.
    2. Grigorieva, E. & Herings, P.J.J. & Müller, R.J. & Vermeulen, A.J., 2004. "The communication complexity of private value single item auctions," Research Memorandum 050, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    3. Grigorieva, E. & Herings, P.J.J. & Müller, R.J. & Vermeulen, A.J., 2006. "Inefficiency of equilibria in query auctions with continuous valuations," Research Memorandum 017, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    4. Chwe, Michael Suk-Young, 1989. "The discrete bid first auction," Economics Letters, Elsevier, vol. 31(4), pages 303-306, December.
    5. Elena Grigorieva & P. Herings & Rudolf Müller & Dries Vermeulen, 2007. "The private value single item bisection auction," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 30(1), pages 107-118, January.
    6. Rothkopf, Michael H. & Harstad, Ronald M., 1994. "On the role of discrete bid levels in oral auctions," European Journal of Operational Research, Elsevier, vol. 74(3), pages 572-581, May.
    7. Engelbrecht-Wiggans, Richard & Kahn, Charles M., 1991. "Protecting the winner : Second-price versus oral auctions," Economics Letters, Elsevier, vol. 35(3), pages 243-248, March.
    8. Grigorieva, Elena & Herings, P. Jean-Jacques & Müller, Rudolf & Vermeulen, Dries, 2011. "Inefficiency of equilibria in digital mechanisms with continuous valuations," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 541-544.
    9. Peter Cramton, 2004. "Simultaneous Ascending Auction," Papers of Peter Cramton 04mit4, University of Maryland, Department of Economics - Peter Cramton, revised 2004.
    10. Grigorieva,Elena & Herings,Jean-Jacques & Müller,Rudolf & Vermeulen,Dries, 2004. "The communication complexity of private value single item auctions," Research Memorandum 052, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    11. William Vickrey, 1961. "Counterspeculation, Auctions, And Competitive Sealed Tenders," Journal of Finance, American Finance Association, vol. 16(1), pages 8-37, March.
    12. Rothkopf, Michael H & Teisberg, Thomas J & Kahn, Edward P, 1990. "Why Are Vickrey Auctions Rare?," Journal of Political Economy, University of Chicago Press, vol. 98(1), pages 94-109, February.
    13. 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.
    14. Mishra, Debasis & Veeramani, Dharmaraj, 2007. "Vickrey-Dutch procurement auction for multiple items," European Journal of Operational Research, Elsevier, vol. 180(2), pages 617-629, July.
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    1. Grigorieva, Elena & Herings, P. Jean-Jacques & Müller, Rudolf & Vermeulen, Dries, 2011. "Inefficiency of equilibria in digital mechanisms with continuous valuations," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 541-544.

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