IDEAS home Printed from https://ideas.repec.org/p/kse/dpaper/48.html
   My bibliography  Save this paper

On Uniform Conditions for the Existence of Mixed Strategy Equilibria

Author

Listed:
  • Pavlo Prokopovych

    () (Kyiv School of Economics, Kyiv Economic Institute)

  • Nicholas C. Yannelis

    () (University of Iowa/ The University of Manchester)

Abstract

Embarking from the concept of uniform payoff security (Monteiro P.K., Page F.H, J Econ Theory 134: 566-575, 2007), we introduce two other uniform conditions and then study the existence of mixed strategy Nash equilibria in games where the sum of the payoff functions is not necessarily upper semicontinuous.

Suggested Citation

  • Pavlo Prokopovych & Nicholas C. Yannelis, 2012. "On Uniform Conditions for the Existence of Mixed Strategy Equilibria," Discussion Papers 48, Kyiv School of Economics.
  • Handle: RePEc:kse:dpaper:48 Note: Submitted to International Journal of Game Theory
    as

    Download full text from publisher

    File URL: http://repec.kse.org.ua/pdf/KSE_dp48.pdf
    File Function: March 2012
    Download Restriction: no

    References listed on IDEAS

    as
    1. Duggan, John, 2007. "Equilibrium existence for zero-sum games and spatial models of elections," Games and Economic Behavior, Elsevier, vol. 60(1), pages 52-74, July.
    2. Ľuboš Pástor & Robert F. Stambaugh, 2012. "On the Size of the Active Management Industry," Journal of Political Economy, University of Chicago Press, vol. 120(4), pages 740-781.
    3. Michael R. Baye & Guoqiang Tian & Jianxin Zhou, 1993. "Characterizations of the Existence of Equilibria in Games with Discontinuous and Non-quasiconcave Payoffs," Review of Economic Studies, Oxford University Press, vol. 60(4), pages 935-948.
    4. 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), pages 291-305.
    5. Philippe Bich, 2009. "Existence of pure Nash equilibria in discontinuous and non quasiconcave games," Documents de travail du Centre d'Economie de la Sorbonne 09061, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    6. Baye, M.R. & Kovenock, D. & De Vries, C.G., 1993. "The Solution to the Tullock Rent-Seeking Game when r>2: Mixed-Strategy Equilibria and Mean Dissipation Rates," Purdue University Economics Working Papers 1039, Purdue University, Department of Economics.
    7. 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), pages 291-305.
    8. Baye, M.R. & Kovenock, D. & De Vries, C.G., 1993. "The Solution to the Tullock Rent-Seeking Game when R > 2: Mixed Strategy Equilibria and Mean Dissipation Rates," Papers 10-93-9, Pennsylvania State - Department of Economics.
    9. Guilherme Carmona, 2005. "On the existence of equilibria in discontinuous games: three counterexamples," International Journal of Game Theory, Springer;Game Theory Society, pages 181-187.
    10. Pavlo Prokopovych, 2011. "On equilibrium existence in payoff secure games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), pages 5-16.
    11. Philippe Bich, 2009. "Existence of pure Nash equilibria in discontinuous and non quasiconcave games," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00426402, HAL.
    12. Philip Reny, 2011. "Strategic approximations of discontinuous games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), pages 17-29.
    13. Pohan Fong, 2008. "Endogenous Limits on Proposal Power," Discussion Papers 1465, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    14. Philip J. Reny, 1999. "On the Existence of Pure and Mixed Strategy Nash Equilibria in Discontinuous Games," Econometrica, Econometric Society, vol. 67(5), pages 1029-1056, September.
    15. Guilherme Carmona, 2011. "Understanding some recent existence results for discontinuous games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), pages 31-45.
    16. Bagh, Adib, 2010. "Variational convergence: Approximation and existence of equilibria in discontinuous games," Journal of Economic Theory, Elsevier, vol. 145(3), pages 1244-1268, May.
    17. Monteiro, Paulo Klinger & Page Jr, Frank H., 2007. "Uniform payoff security and Nash equilibrium in compact games," Journal of Economic Theory, Elsevier, vol. 134(1), pages 566-575, May.
    18. Leo K. Simon, 1987. "Games with Discontinuous Payoffs," Review of Economic Studies, Oxford University Press, vol. 54(4), pages 569-597.
    19. Andrew McLennan & Paulo K. Monteiro & Rabee Tourky, 2011. "Games With Discontinuous Payoffs: A Strengthening of Reny's Existence Theorem," Econometrica, Econometric Society, vol. 79(5), pages 1643-1664, September.
    20. Pavlo Prokopovych, 2013. "The single deviation property in games with discontinuous payoffs," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), pages 383-402.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. repec:spr:etbull:v:2:y:2014:i:1:d:10.1007_s40505-013-0021-5 is not listed on IDEAS
    2. Allison, Blake A. & Lepore, Jason J., 2014. "Verifying payoff security in the mixed extension of discontinuous games," Journal of Economic Theory, Elsevier, vol. 152(C), pages 291-303.

    More about this item

    Keywords

    Discontinuous game; Diagonally transfer continuous game; Payoff secure game; Mixed strategy equilibrium; Transfer lower semicontinuity;

    JEL classification:

    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:kse:dpaper:48. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Iryna Sobetska). General contact details of provider: http://edirc.repec.org/data/ksecoua.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.