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Sequential equilibria of asymmetric ascending auctions: The case of log-normal distributions


  • Robert Wilson

    () (Business School, Stanford University, Stanford, CA 94305-5015, USA)


The sequential equilibrium of an ascending-price auction of a single item is derived explicitly for the case of log-normal distributions and a multiplicative valuation model comprising both common and private factors, and allowing asymmetries. If the prior distribution on the common factors is diffuse, or of the form obtained by Bayesian updating from a diffuse prior distribution, then the equilibrium strategies are log-linear with coefficients obtained by solving a set of linear equations. A similar construction applies to normal distributions and additive terms in the valuation model. An example illustrates the predictions derived from the model.

Suggested Citation

  • Robert Wilson, 1998. "Sequential equilibria of asymmetric ascending auctions: The case of log-normal distributions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 12(2), pages 433-440.
  • Handle: RePEc:spr:joecth:v:12:y:1998:i:2:p:433-440 Note: Received: December 11, 1996; revised version: July 15, 1997

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    References listed on IDEAS

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    Cited by:

    1. Li, Tong & Perrigne, Isabelle & Vuong, Quang, 2000. "Conditionally independent private information in OCS wildcat auctions," Journal of Econometrics, Elsevier, vol. 98(1), pages 129-161, September.
    2. Hong, Han & Shum, Matthew, 2003. "Econometric models of asymmetric ascending auctions," Journal of Econometrics, Elsevier, vol. 112(2), pages 327-358, February.
    3. Dubra, Juan & Echenique, Federico & Manelli, Alejandro M., 2009. "English auctions and the Stolper-Samuelson theorem," Journal of Economic Theory, Elsevier, vol. 144(2), pages 825-849, March.
    4. Jonathan B. Hill & Artyom Shneyerov, 2009. "Are There Common Values in BC Timber Sales? A Tail-Index Nonparametric Test," Working Papers 09003, Concordia University, Department of Economics.
    5. Dakshina Garfield De Silva & Marina Gertsberg & Georgia Kosmopoulou & Rachel Pownall, 2017. "Dealer Networks in the World of Art," Working Papers 198144199, Lancaster University Management School, Economics Department.
    6. Audrey Hu & Theo Offerman & Liang Zou, 2014. "How Risk Sharing may enhance Efficiency in English Auctions," Tinbergen Institute Discussion Papers 14-015/I, Tinbergen Institute.
    7. Hill, Jonathan B. & Shneyerov, Artyom, 2013. "Are there common values in first-price auctions? A tail-index nonparametric test," Journal of Econometrics, Elsevier, vol. 174(2), pages 144-164.
    8. Krishna, Vijay, 2003. "Asymmetric English auctions," Journal of Economic Theory, Elsevier, vol. 112(2), pages 261-288, October.
    9. M. Yenmez, 2014. "Pricing in position auctions and online advertising," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 55(1), pages 243-256, January.
    10. Susan Athey & Philip A. Haile, 2002. "Identification of Standard Auction Models," Econometrica, Econometric Society, vol. 70(6), pages 2107-2140, November.
    11. Haile, Philip A., 2003. "Auctions with private uncertainty and resale opportunities," Journal of Economic Theory, Elsevier, vol. 108(1), pages 72-110, January.
    12. Lorentziadis, Panos L., 2016. "Optimal bidding in auctions from a game theory perspective," European Journal of Operational Research, Elsevier, vol. 248(2), pages 347-371.
    13. Satterthwaite, Mark A. & Williams, Steven R. & Zachariadis, Konstantinos E., 2014. "Optimality versus practicality in market design: A comparison of two double auctions," Games and Economic Behavior, Elsevier, vol. 86(C), pages 248-263.
    14. Echenique, Federico & Manelli, Alejandro M., 2003. "Comparative Statics, English Auctions, and the Stolper-Samuelson Theorem," Working Papers 1178, California Institute of Technology, Division of the Humanities and Social Sciences.

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