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The Complete Information First. Price Auction or the Importance of Being Indivisible

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  • Alcalde, José
  • Dahm, Matthias

Abstract

Abstract Despite the popularity of auction theoretical thinking, it appears that no one has presented an elementary equilibrium analysis of the first-price sealed-bid auction mechanism under complete information. This paper aims to remedy that omission. We show that the existence of pure strategy undominated Nash equilibria requires that the bidding space is not "too divisible" (that is, a continuum). In fact, when bids must form part of a finite grid there always exists a "high price equilibrium". However, there might also be "low price equilibria" and when the bidding space is very restrictive the revenue obtained in these "low price equilibria" might be very low. We discuss the properties of the equilibria and an application of auction theoretical thinking in which "low price equilibria" may be relevant. Keywords: First-price auctions, undominated Nash equilibria. JEL Classification Numbers: C72 (Noncooperative Games), D44 (Auctions).

Suggested Citation

  • Alcalde, José & Dahm, Matthias, 2008. "The Complete Information First. Price Auction or the Importance of Being Indivisible," Working Papers 2072/13264, Universitat Rovira i Virgili, Department of Economics.
  • Handle: RePEc:urv:wpaper:2072/13264
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    References listed on IDEAS

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    6. Martin Shubik, 1971. "The Dollar Auction game: a paradox in noncooperative behavior and escalation," Journal of Conflict Resolution, Peace Science Society (International), vol. 15(1), pages 109-111, March.
    7. Baye, Michael R & Kovenock, Dan & de Vries, Casper G, 1993. "Rigging the Lobbying Process: An Application of the All-Pay Auction," American Economic Review, American Economic Association, vol. 83(1), pages 289-294, March.
    8. Wedad Elmaghraby & Shmuel S. Oren, 1999. "The Efficiency of Multi-Unit Electricity Auctions," The Energy Journal, International Association for Energy Economics, vol. 0(Number 4), pages 89-116.
    9. Chwe, Michael Suk-Young, 1989. "The discrete bid first auction," Economics Letters, Elsevier, vol. 31(4), pages 303-306, December.
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    11. Milgrom, Paul R & Weber, Robert J, 1982. "A Theory of Auctions and Competitive Bidding," Econometrica, Econometric Society, vol. 50(5), pages 1089-1122, September.
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    Cited by:

    1. José Alcalde & Matthias Dahm, 2011. "On The Complete Information First-Price Auction And Its Intuitive Solution," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 13(03), pages 353-361.

    More about this item

    Keywords

    Jocs; Teoria de; Preus -- Fixació; Equilibri (Economia); Nash; Varietats de; 338 - Situació econòmica. Política econòmica. Gestió; control i planificació de l'economia. Producció. Serveis. Turisme. Preus;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions

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