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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. Baye, M.R. & Kovenock, D. & De Vries, C.G., 1992. "Rigging the Lobbying Process: An Application of the All- Pay Auction," Papers 9-92-2, Pennsylvania State - Department of Economics.
  2. Moldovanu, Benny & Sela, Aner, 1998. "Patent Licensing to Bertrand Competitors," Sonderforschungsbereich 504 Publications 98-21, Sonderforschungsbereich 504, Universität Mannheim;Sonderforschungsbereich 504, University of Mannheim.
  3. 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.
  4. 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.
  5. 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.
  6. Baye, M.R. & Kovenock, D. & De Vries, C.G., 1991. "The All-Pay Auction With Complete Information," Purdue University Economics Working Papers 1007, Purdue University, Department of Economics.
  7. Simon, Leo K & Zame, William R, 1990. "Discontinuous Games and Endogenous Sharing Rules," Econometrica, Econometric Society, vol. 58(4), pages 861-72, July.
  8. Blume, Andreas, 2003. "Bertrand without fudge," Economics Letters, Elsevier, vol. 78(2), pages 167-168, February.
  9. Kala Krishna & Torben Tranæ s, 2002. "Allocating multiple units," Economic Theory, Springer, vol. 20(4), pages 733-750.
  10. Chwe, Michael Suk-Young, 1989. "The discrete bid first auction," Economics Letters, Elsevier, vol. 31(4), pages 303-306, December.
  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. Flavio M. Menezes, 2003. "An auction theoretical approach to fiscal wars," Social Choice and Welfare, Springer, vol. 20(1), pages 155-166.
  13. Taylor, Leon, 1992. "Infrastructural competition among jurisdictions," Journal of Public Economics, Elsevier, vol. 49(2), pages 241-259, November.
  14. 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.
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