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

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  • 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.

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File URL: http://repec.kse.org.ua/pdf/KSE_dp12.pdf
File Function: December 2008
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Bibliographic Info

Paper provided by Kyiv School of Economics in its series Discussion Papers with number 12.

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Date of creation: Dec 2008
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Handle: RePEc:kse:dpaper:12

Note: Published in Economic Theory DOI 10.1007/s00199-010-0526-1S
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Related research

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

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  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. Baye, Michael R & Tian, Guoqiang & Zhou, Jianxin, 1993. "Characterizations of the Existence of Equilibria in Games with Discontinuous and Non-quasiconcave Payoffs," Review of Economic Studies, Wiley Blackwell, vol. 60(4), pages 935-48, October.
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