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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, 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.
  2. Baye, M.R. & Kovenock, D. & De Vries, C., 1992. "The All-Pay Auction with Complete Information," Papers 8-92-1, Pennsylvania State - Department of Economics.
  3. 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.
  4. Milgrom, Paul R & Weber, Robert J, 1982. "A Theory of Auctions and Competitive Bidding," Econometrica, Econometric Society, vol. 50(5), pages 1089-1122, September.
  5. Blume, Andreas, 2003. "Bertrand without fudge," Economics Letters, Elsevier, vol. 78(2), pages 167-168, February.
  6. Jean-Pierre Benoît & Vijay Krishna, 2001. "Multiple-Object Auctions with Budget Constrained Bidders," Review of Economic Studies, Oxford University Press, vol. 68(1), pages 155-179.
  7. 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.
  8. Grimm, Veronika & Riedel, Frank & Wolfstetter, Elmar, 2003. "Low price equilibrium in multi-unit auctions: the GSM spectrum auction in Germany," International Journal of Industrial Organization, Elsevier, vol. 21(10), pages 1557-1569, December.
  9. Chwe, Michael Suk-Young, 1989. "The discrete bid first auction," Economics Letters, Elsevier, vol. 31(4), pages 303-306, December.
  10. Menezes, Flavio Marques, 2000. "An auction theoretical approach to fiscal wars," Economics Working Papers (Ensaios Economicos da EPGE) 406, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
  11. Simon, Leo K. & Zame, William R., 1987. "Discontinous Games and Endogenous Sharing Rules," Department of Economics, Working Paper Series qt8n46v2wv, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
  12. Moldovanu, Benny & Sela, Aner, 2003. "Patent licensing to Bertrand competitors," International Journal of Industrial Organization, Elsevier, vol. 21(1), pages 1-13, January.
  13. Taylor, Leon, 1992. "Infrastructural competition among jurisdictions," Journal of Public Economics, Elsevier, vol. 49(2), pages 241-259, November.
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