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On the Complete Information First--Price Auction and its Intuitive Solution

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  • Alcalde, Jose
  • Dahm, Matthias

Abstract

Despite the popularity of auction theoretical thinking, it appears that no one has presented an elementary equilibrium analysis of the complete information first-price sealed-bid auction mechanism when the bidding space has a finite grid. This paper aims to remedy that omission. We show that there always exists a "high price equilibrium" which can be considered "the intuitive solution" (an agent with the highest valuation wins the auction bidding at the second-highest valuation). Although there might be other "low price equilibria", we also show that when there are two bidders "the intuitive solution" is the unique limiting equilibrium when the grid size goes to zero and ties are randomly broken.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 22306.

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Date of creation: 14 Mar 2010
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Handle: RePEc:pra:mprapa:22306

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Keywords: First-price auctions; undominated Nash equilibria.;

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References

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  1. Chwe, Michael Suk-Young, 1989. "The discrete bid first auction," Economics Letters, Elsevier, vol. 31(4), pages 303-306, December.
  2. 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.
  3. Moldovanu, Benny & Sela, Aner, 1998. "Patent Licensing to Bertrand Competitors," Sonderforschungsbereich 504 Publications 98-21, Sonderforschungsbereich 504, Universität Mannheim & Sonderforschungsbereich 504, University of Mannheim.
  4. Rapoport, Amnon & Amaldoss, Wilfred, 2004. "Mixed-strategy play in single-stage first-price all-pay auctions with symmetric players," Journal of Economic Behavior & Organization, Elsevier, vol. 54(4), pages 585-607, August.
  5. 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.
  6. Jean-Pierre Benoit & Vijay Krishna, 1998. "Multiple-Object Auctions with Budget Constrained Bidders," Game Theory and Information 9805001, EconWPA, revised 26 Jul 1999.
  7. James J. Anton & Dennis A. Yao, 1989. "Split Awards, Procurement, and Innovation," RAND Journal of Economics, The RAND Corporation, vol. 20(4), pages 538-552, Winter.
  8. Bernheim, B Douglas & Whinston, Michael D, 1986. "Menu Auctions, Resource Allocation, and Economic Influence," The Quarterly Journal of Economics, MIT Press, vol. 101(1), pages 1-31, February.
  9. 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.
  10. 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.
  11. Kala Krishna & Torben Tranæ s, 2002. "Allocating multiple units," Economic Theory, Springer, vol. 20(4), pages 733-750.
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Cited by:
  1. Alcalde, José & Dahm, Matthias, 2013. "Competition for procurement shares," Games and Economic Behavior, Elsevier, vol. 80(C), pages 193-208.
  2. Matthias Dahm & Robert Dur & Amihai Glazer, 2012. "How a Firm Can Induce Legislators to Adopt a Bad Policy," CESifo Working Paper Series 3788, CESifo Group Munich.

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