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Continuity of the first price auction Nash equilibrium correspondence

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  • 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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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. Todd R. Kaplan & Shmuel Zamir, 2014. "Advances in Auctions," Discussion Papers 1405, Exeter University, Department of Economics.
    4. Thomas, Charles J., 2011. "Vertical mergers in procurement markets," International Journal of Industrial Organization, Elsevier, vol. 29(2), pages 200-209, March.
    5. 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.
    6. Kaplan, Todd R. & Zamir, Shmuel, 2015. "Advances in Auctions," Handbook of Game Theory with Economic Applications, Elsevier.
    7. 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.
    8. 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.
    9. Bernard Lebrun, 2004. "Optimality And The Second-Price Auction With Resale," Discussion Papers 2004_03, York University, Department of Economics, revised May 2004.
    10. Cole, Matthew T. & Davies, Ronald B. & Kaplan, Todd, 2017. "Protection in government procurement auctions," Journal of International Economics, Elsevier, pages 134-142.
    11. 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.
    12. 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.
    13. 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.;

    JEL classification:

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

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