A Short Proof of Reny's Existence Theorem for Payoff Secure Games
AbstractA 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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Bibliographic InfoPaper provided by Kyiv School of Economics in its series Discussion Papers with number 12.
Date of creation: Dec 2008
Date of revision:
Note: Published in Economic Theory DOI 10.1007/s00199-010-0526-1S
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Discontinuous game; payoff security; transfer lower semicontinuity; approximate Nash equilibrium; Reny's theorem;
Find related papers by 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
This paper has been announced in the following NEP Reports:
- NEP-ALL-2008-12-21 (All new papers)
- NEP-GTH-2008-12-21 (Game Theory)
- NEP-HPE-2008-12-21 (History & Philosophy of Economics)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- 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.
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