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First-Price Auctions when the Ranking of Valuations

Author

Listed:
  • Elmar Wolfstetter

    (Humboldt University of Berlin)

  • Michael Landsberger

    (Hiafa University Israel)

  • Jakob Rubinstei

    (Hiafa University Israel)

  • Shmuel Zamir

    (Hebrew University, Jerusalem)

Abstract

We consider an augmented version of the symmetric private value auction model with independent types. The augmentation, intended to illustrate reality, concerns information bidders have about their opponents. To the standard assumption that every bidder knows his type and the distribution of types is common knowledge we add the assumption that the ranking of bidders' valuations is common knowledge. This set-up induces a particular asymmetric auction model that raises serious technical difficulties. We prove existence and uniqueness of equilibrium in pure strategies in the two bidder case. We also show that the model generally has no analytic solution. If the distribution of valuations is uniform, both bidders bid pointwise more aggressively relative to the standard symmetric case. However, this property does not apply to all distributions of valuations. Finally, we also provide a numerical solution of equilibrium bid functions for the uniform distribution case.

Suggested Citation

  • Elmar Wolfstetter & Michael Landsberger & Jakob Rubinstei & Shmuel Zamir, 1997. "First-Price Auctions when the Ranking of Valuations," Microeconomics 9701004, EconWPA.
  • Handle: RePEc:wpa:wuwpmi:9701004
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    References listed on IDEAS

    as
    1. Eric Maskin & John Riley, 2000. "Equilibrium in Sealed High Bid Auctions," Review of Economic Studies, Oxford University Press, vol. 67(3), pages 439-454.
    2. Wolfstetter, Elmar, 1996. " Auctions: An Introduction," Journal of Economic Surveys, Wiley Blackwell, vol. 10(4), pages 367-420, December.
    3. Milgrom, Paul R & Weber, Robert J, 1982. "A Theory of Auctions and Competitive Bidding," Econometrica, Econometric Society, vol. 50(5), pages 1089-1122, September.
    4. Milgrom, Paul, 1989. "Auctions and Bidding: A Primer," Journal of Economic Perspectives, American Economic Association, vol. 3(3), pages 3-22, Summer.
    5. McAfee, R Preston & McMillan, John, 1987. "Auctions and Bidding," Journal of Economic Literature, American Economic Association, vol. 25(2), pages 699-738, June.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Chouinard Hayley H & Yoder Jonathan K, 2007. "Repeated Auctions with the Right of First Refusal," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 7(1), pages 1-15, June.
    2. Elbittar, Alexander, 2009. "Impact of valuation ranking information on bidding in first-price auctions: A laboratory study," Journal of Economic Behavior & Organization, Elsevier, vol. 69(1), pages 75-85, January.
    3. Rene Kirkegaard, 2005. "A Simple Approach to Analyzing Asymmetric First Price Auctions," Working Papers 0504, Brock University, Department of Economics, revised Nov 2005.
    4. Wolfstetter, Elmar, 2001. "The Swiss UMTS spectrum auction flop: Bad luck or bad design?," SFB 373 Discussion Papers 2001,50, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    5. Perry, Motty & Wolfstetter, Elmar & Zamir, Shmuel, 2000. "A Sealed-Bid Auction That Matches the English Auction," Games and Economic Behavior, Elsevier, vol. 33(2), pages 265-273, November.
    6. Hayley Chouinard, 2006. "Repeated Auctions with the Right of First Refusal and Asymmetric Information," Working Papers 2006-6, School of Economic Sciences, Washington State University.

    More about this item

    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions

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