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Non-Existence of Equilibrium in Vickrey, Second-Price, and English Auctions


  • Jackson, Matthew O.


A simple example shows that equilibria can fail to exist in second price (Vickrey) and English auctions when there are both common and private components to bidders' valuations and private information is held on both dimensions. The example shows that equilibrium only exists in the extremes of pure private and pure common values, and that existence in standard models is not robust to a slight perturbation.

Suggested Citation

  • Jackson, Matthew O., 2005. "Non-Existence of Equilibrium in Vickrey, Second-Price, and English Auctions," Working Papers 1241, California Institute of Technology, Division of the Humanities and Social Sciences.
  • Handle: RePEc:clt:sswopa:1241

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    References listed on IDEAS

    1. Eric Maskin & John Riley, 2000. "Equilibrium in Sealed High Bid Auctions," Review of Economic Studies, Oxford University Press, vol. 67(3), pages 439-454.
    2. Simon, Leo K & Zame, William R, 1990. "Discontinuous Games and Endogenous Sharing Rules," Econometrica, Econometric Society, vol. 58(4), pages 861-872, July.
    3. Matthew O. Jackson & Leo K. Simon & Jeroen M. Swinkels & William R. Zame, 2002. "Communication and Equilibrium in Discontinuous Games of Incomplete Information," Econometrica, Econometric Society, vol. 70(5), pages 1711-1740, September.
    4. Milgrom, Paul R & Weber, Robert J, 1982. "A Theory of Auctions and Competitive Bidding," Econometrica, Econometric Society, vol. 50(5), pages 1089-1122, September.
    5. Aloisio Araujo & Luciano I. de Castro Filho, 2004. "Pure Strategy Equilibria of Multidimensional and Non-Monotonic Auctions," Econometric Society 2004 Latin American Meetings 300, Econometric Society.
    6. Jeroen M. Swinkels & Wolfgang Pesendorfer, 2000. "Efficiency and Information Aggregation in Auctions," American Economic Review, American Economic Association, vol. 90(3), pages 499-525, June.
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    Cited by:

    1. Luciano De Castro, 2012. "Correlation of Types in Bayesian Games," Discussion Papers 1556, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    2. Gagan Ghosh, 2015. "Non-existence of equilibria in simultaneous auctions with a common budget-constraint," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(2), pages 253-274, May.
    3. Vlad Mares & Mikhael Shor, 2013. "Information concentration in common value environments," Review of Economic Design, Springer;Society for Economic Design, vol. 17(3), pages 183-203, September.
    4. Rabia Nessah & Guoqiang Tian, 2016. "On the existence of Nash equilibrium in discontinuous games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(3), pages 515-540, March.
    5. Tian, Guoqiang, 2015. "On the existence of equilibria in games with arbitrary strategy spaces and preferences," Journal of Mathematical Economics, Elsevier, vol. 60(C), pages 9-16.
    6. Tan, Xu, 2016. "Information revelation in auctions with common and private values," Games and Economic Behavior, Elsevier, vol. 97(C), pages 147-165.
    7. repec:hal:journl:halshs-00717135 is not listed on IDEAS
    8. Philippe Bich & Rida Laraki, 2012. "A Unified Approach to Equilibrium Existence in Discontinuous Strategic Games," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00717135, HAL.
    9. Philippe Bich & Rida Laraki, 2014. "On the Existence of Approximate Equilibria and Sharing Rule Solutions in Discontinuous Games," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-01071678, HAL.
    10. 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.
    11. Philippe Bich & Rida Laraki, 2013. "On the Existence of Approximated Equilibria and Sharing-Rule Equilibria in Discontinuous Games," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00846143, HAL.
    12. repec:eee:indorg:v:52:y:2017:i:c:p:282-306 is not listed on IDEAS
    13. Philippe Bich & Rida Laraki, 2012. "A Unified Approach to Equilibrium Existence in Discontinuous Strategic Games," Documents de travail du Centre d'Economie de la Sorbonne 12040, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    14. Oriol Carbonell-Nicolau & Richard McLean, 2014. "On the existence of Nash equilibrium in Bayesian games," Departmental Working Papers 201402, Rutgers University, Department of Economics.
    15. Tan, Xu & Xing, Yiqing, 2011. "Auctions with both common-value and private-value bidders," Economics Letters, Elsevier, vol. 111(1), pages 99-103, April.

    More about this item


    general equilibrium; stability; experiments;

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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