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A Short Proof of Reny's Existence Theorem for Payoff Secure Games

Author

Listed:
  • Pavlo Prokopovych

    () (Kyiv School of Economics and Kyiv Economics Institute)

Abstract

A short proof of Reny (1999)'s equilibrium existence theorem for payoff secure games is provided. At the heart of the proof lies the concept of a multivalued mapping with the local intersection property. By means of the Fan-Browder collective fixed-point theorem, we show an approximate equilibrium existence theorem which covers a number of known games. Reny's theorem follows from it straightforwardly.

Suggested Citation

  • Pavlo Prokopovych, 2008. "A Short Proof of Reny's Existence Theorem for Payoff Secure Games," Discussion Papers 12, Kyiv School of Economics.
  • Handle: RePEc:kse:dpaper:12
    Note: Published in Economic Theory DOI 10.1007/s00199-010-0526-1S
    as

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    File URL: http://repec.kse.org.ua/pdf/KSE_dp12.pdf
    File Function: December 2008
    Download Restriction: no

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Adib Bagh & Alejandro Jofre, 2006. "Reciprocal Upper Semicontinuity and Better Reply Secure Games: A Comment," Econometrica, Econometric Society, vol. 74(6), pages 1715-1721, November.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    Discontinuous game; payoff security; transfer lower semicontinuity; approximate Nash equilibrium; Reny's theorem;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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