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


  • Alcalde, Jose
  • Dahm, Matthias


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.

Suggested Citation

  • Alcalde, Jose & Dahm, Matthias, 2010. "On the Complete Information First--Price Auction and its Intuitive Solution," MPRA Paper 22306, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:22306

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    References listed on IDEAS

    1. Simon, Leo K & Zame, William R, 1990. "Discontinuous Games and Endogenous Sharing Rules," Econometrica, Econometric Society, vol. 58(4), pages 861-872, July.
    2. Dan Kovenock & Michael R. Baye & Casper G. de Vries, 1996. "The all-pay auction with complete information (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(2), pages 291-305.
    3. Moldovanu, Benny & Sela, Aner, 2003. "Patent licensing to Bertrand competitors," International Journal of Industrial Organization, Elsevier, vol. 21(1), pages 1-13, January.
    4. Barry O'neill, 1986. "International Escalation and the Dollar Auction," Journal of Conflict Resolution, Peace Science Society (International), vol. 30(1), pages 33-50, March.
    5. B. Douglas Bernheim & Michael D. Whinston, 1986. "Menu Auctions, Resource Allocation, and Economic Influence," The Quarterly Journal of Economics, Oxford University Press, vol. 101(1), pages 1-31.
    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. Krishna, Vijay, 2009. "Auction Theory," Elsevier Monographs, Elsevier, edition 2, number 9780123745071.
    8. 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 289-294, March.
    9. 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.
    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. 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.
    12. Chwe, Michael Suk-Young, 1989. "The discrete bid first auction," Economics Letters, Elsevier, vol. 31(4), pages 303-306, December.
    13. Kala Krishna & Torben Tranæ s, 2002. "Allocating multiple units," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), 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, 2014. "How a firm can induce legislators to adopt a bad policy," Public Choice, Springer, vol. 159(1), pages 63-82, April.

    More about this item


    First-price auctions; undominated Nash equilibria.;

    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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