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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).

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Bibliographic Info

Paper provided by Universitat Rovira i Virgili, Department of Economics in its series Working Papers with number 2072/13264.

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Date of creation: 2008
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Handle: RePEc:urv:wpaper:2072/13264

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Related research

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;

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References

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  1. Kovenock, D. & de Vries, C.G., 1995. "The All-Pay Auction with Complete Information," UFAE and IAE Working Papers 311.95, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  2. M. Landsberger & J. Rubinstein & E. Wolfstetter & S. Zamir, 1996. "First-Price Auctions when the Ranking of Valuations is Common Knowledge," SFB 373 Discussion Papers 1996,36, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  3. Benoit, Jean-Pierre & Krishna, Vijay, 2001. "Multiple-Object Auctions with Budget Constrained Bidders," Review of Economic Studies, Wiley Blackwell, vol. 68(1), pages 155-79, January.
  4. Leo K. Simon and William R. Zame., 1987. "Discontinuous Games and Endogenous Sharing Rules," Economics Working Papers 8756, University of California at Berkeley.
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  6. Taylor, Leon, 1992. "Infrastructural competition among jurisdictions," Journal of Public Economics, Elsevier, vol. 49(2), pages 241-259, November.
  7. Veronika Grimm & Frank Riedel & Elmar G. Wolfstetter, 2001. "Low Price Equilibrium in Multi-Unit Auctions: The GSM Spectrum Auction in Germany," CESifo Working Paper Series 506, CESifo Group Munich.
  8. Blume, Andreas, 2003. "Bertrand without fudge," Economics Letters, Elsevier, vol. 78(2), pages 167-168, February.
  9. 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.
  10. Kala Krishna & Torben Tranæ s, 2002. "Allocating multiple units," Economic Theory, Springer, vol. 20(4), pages 733-750.
  11. 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.
  12. Chwe, Michael Suk-Young, 1989. "The discrete bid first auction," Economics Letters, Elsevier, vol. 31(4), pages 303-306, December.
  13. 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 289-94, March.
  14. Flavio M. Menezes, 2003. "An auction theoretical approach to fiscal wars," Social Choice and Welfare, Springer, vol. 20(1), pages 155-166.
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Cited by:
  1. Alcalde, Jose & Dahm, Matthias, 2010. "On the Complete Information First--Price Auction and its Intuitive Solution," MPRA Paper 22306, University Library of Munich, Germany.

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