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Domain L-Majorization and Equilibrium Existence in Discontinuous Games

Author

Listed:
  • Pavlo Prokopovych

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

Abstract

We study the equilibrium existence problem in normal form and qualitative games in which it is possible to associate with each nonequilibrium point an open neighborhood and a collection of deviation strategies such that, at any nonequilibrium point of the neighborhood, a player can increase her payoff by switching to the deviation strategy designated for her. An equilibrium existence theorem for compact, quasiconcave games with two players is established. We propose a new form of the better-reply security condition, called the strong single deviation property, that covers games whose set of Nash equilibria is not necessarily closed. We introduce domain L-majorized correspondences and use them to study equilibrium existence in qualitative games.

Suggested Citation

  • Pavlo Prokopovych, 2010. "Domain L-Majorization and Equilibrium Existence in Discontinuous Games," Discussion Papers 31, Kyiv School of Economics, revised May 2011.
  • Handle: RePEc:kse:dpaper:31
    Note: Revised and resubmitted to Economic Theory
    as

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    File URL: http://repec.kse.org.ua/pdf/KSE_dp31.pdf
    File Function: Revised version, May 2011
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    References listed on IDEAS

    as
    1. Yannelis, Nicholas C. & Prabhakar, N. D., 1983. "Existence of maximal elements and equilibria in linear topological spaces," Journal of Mathematical Economics, Elsevier, vol. 12(3), pages 233-245, December.
    2. Pavlo Prokopovych, 2011. "On equilibrium existence in payoff secure games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(1), pages 5-16, September.
    3. 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.
    4. Guilherme Carmona, 2011. "Understanding some recent existence results for discontinuous games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(1), pages 31-45, September.
    5. Nessah, Rabia & Tian, Guoqiang, 2008. "Existence of Equilibria in Discontinuous Games," MPRA Paper 41206, University Library of Munich, Germany, revised Mar 2010.
    6. 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.
    7. Luciano I. de Castro, 2008. "Equilibria Existence in Regular Discontinuous Games," Discussion Papers 1463, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    8. Bagh, Adib, 1998. "Equilibrium in abstract economies without the lower semi-continuity of the constraint maps," Journal of Mathematical Economics, Elsevier, vol. 30(2), pages 175-185, September.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    Majorized correspondence; Qualitative game; Discontinuous game; Better-reply security; Single deviation property;

    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

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