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

  • Alcalde, José
  • Dahm, Matthias

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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File URL: http://hdl.handle.net/2072/13264
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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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  1. Grimm, Veronika & Riedel, Frank & Wolfstetter, Elmar, 2001. "Low price equilibrium in multi-unit auctions: The GSM spectrum auction in Germany," SFB 373 Discussion Papers 2001,31, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  2. Milgrom, Paul R & Weber, Robert J, 1982. "A Theory of Auctions and Competitive Bidding," Econometrica, Econometric Society, vol. 50(5), pages 1089-1122, September.
  3. Michael Landsberger & Jacob Rubinstein & Elmar Wolfstetter & Shmuel Zamir, 1999. "First-Price Auctions when the Ranking of Valuations is Common Knowledge," Working Papers 99-18, Centre de Recherche en Economie et Statistique.
  4. 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.
  5. Dan Kovenock & Michael R. Baye & Casper G. de Vries, 1996. "The all-pay auction with complete information (*)," Economic Theory, Springer, vol. 8(2), pages 291-305.
  6. Simon, Leo K & Zame, William R, 1990. "Discontinuous Games and Endogenous Sharing Rules," Econometrica, Econometric Society, vol. 58(4), pages 861-72, July.
  7. Taylor, Leon, 1992. "Infrastructural competition among jurisdictions," Journal of Public Economics, Elsevier, vol. 49(2), pages 241-259, November.
  8. 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.
  9. Baye, M.R. & Kovenock, D. & De Vries, C.G., 1991. "Rigging The Lobbying Process: An Application Of The All- Pay Auction," Purdue University Economics Working Papers 1002, Purdue University, Department of Economics.
  10. Moldovanu, Benny & Sela, Aner, 1998. "Patent Licensing to Bertrand Competitors," Sonderforschungsbereich 504 Publications 98-21, Sonderforschungsbereich 504, Universität Mannheim;Sonderforschungsbereich 504, University of Mannheim.
  11. Chwe, Michael Suk-Young, 1989. "The discrete bid first auction," Economics Letters, Elsevier, vol. 31(4), pages 303-306, December.
  12. Kala Krishna & Torben Tranæ s, 2002. "Allocating multiple units," Economic Theory, Springer, vol. 20(4), pages 733-750.
  13. Flavio M. Menezes, 2003. "An auction theoretical approach to fiscal wars," Social Choice and Welfare, Springer, vol. 20(1), pages 155-166.
  14. Blume, Andreas, 2003. "Bertrand without fudge," Economics Letters, Elsevier, vol. 78(2), pages 167-168, February.
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