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Continuity of the first price auction Nash equilibrium correspondence

Author

Listed:
  • Bernard Lebrun

    (Département d'économique, Université Laval, Pavillon J.-A.-De Sève, Québec, G1K 7P4, CANADA)

Abstract

Despite the complexity of the first price auction in the general asymmetric case, analytical results have started to emerge in the literature. Authors have also searched to gain insights by computing numerical estimates of the equilibria for some probability distributions of the valuations. This paper proves that the Nash equilibrium of the first price auction depends continuously, for the weak topology, on the valuation distributions and thus brings robustness to the numerical results as well as some theoretical results. As an example of application, we disprove a conjecture of comparative statics.

Suggested Citation

  • Bernard Lebrun, 2002. "Continuity of the first price auction Nash equilibrium correspondence," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 20(3), pages 435-453.
    • Handle: RePEc:spr:joecth:v:20:y:2002:i:3:p:435-453
    Note: Received: February 1, 1999; revised version: July 27, 2001
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    Cited by:

    1. Thomas, Charles J., 2011. "Vertical mergers in procurement markets," International Journal of Industrial Organization, Elsevier, vol. 29(2), pages 200-209, March.
    2. Imhof, David, 2017. "Simple Statistical Screens to Detect Bid Rigging," FSES Working Papers 484, Faculty of Economics and Social Sciences, University of Freiburg/Fribourg Switzerland.
    3. Lebrun, Bernard, 2006. "Uniqueness of the equilibrium in first-price auctions," Games and Economic Behavior, Elsevier, vol. 55(1), pages 131-151, April.
    4. Kirkegaard, René, 2021. "Ranking reversals in asymmetric auctions," Journal of Mathematical Economics, Elsevier, vol. 95(C).
    5. Doni Nicola & Menicucci Domenico, 2013. "Revenue Comparison in Asymmetric Auctions with Discrete Valuations," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 13(1), pages 429-461, September.
    6. Kaplan, Todd R. & Zamir, Shmuel, 2015. "Advances in Auctions," Handbook of Game Theory with Economic Applications,, Elsevier.
    7. Bernard Lebrun, 2004. "Optimality And The Second-Price Auction With Resale," Discussion Papers 2004_03, York University, Department of Economics, revised May 2004.
    8. Muhammed Ceesay & Nicola Doni & Domenico Menicucci, 2024. "Asymmetric Auctions with Discretely Distributed Valuations," Working Papers - Economics wp2024_20.rdf, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa.
    9. Bernard Lebrun, 2015. "Revenue-superior variants of the second-price auction," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 59(2), pages 245-275, June.
    10. Sumit Joshi & Poorvi Vora, 2013. "Weak and strong multimarket bidding rings," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 53(3), pages 657-696, August.
    11. Cole, Matthew T. & Davies, Ronald B. & Kaplan, Todd, 2017. "Protection in government procurement auctions," Journal of International Economics, Elsevier, vol. 106(C), pages 134-142.
    12. Imhof, David, 2017. "Econometric tests to detect bid-rigging cartels: does it work?," FSES Working Papers 483, Faculty of Economics and Social Sciences, University of Freiburg/Fribourg Switzerland.
    13. Hsueh, Shao-Chieh & Tian, Guoqiang, 2009. "Nonratifiability of the Cartel Mechanism in First-Price Sealed-Bid Auction with Participation Costs," MPRA Paper 41202, University Library of Munich, Germany, revised Oct 2010.
    14. Olivier Armantier & Jean-Pierre Florens & Jean-Francois Richard, 2008. "Approximation of Nash equilibria in Bayesian games," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 23(7), pages 965-981.
    15. Todd Kaplan & Shmuel Zamir, 2012. "Asymmetric first-price auctions with uniform distributions: analytic solutions to the general case," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 50(2), pages 269-302, June.
    16. Cheng, Harrison, 2011. "Asymmetry and revenue in first-price auctions," Economics Letters, Elsevier, vol. 111(1), pages 78-80, April.

    More about this item

    Keywords

    First price auctions; Nash equilibrium correspondence; Robustness of numerical and theoretical results.;
    All these keywords.

    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions

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