A constructive and elementary proof of Reny's theorem
AbstractIn a recent but well known paper, Reny proved the existence of Nash equilibria for better-reply-secure games, with possibly discontinuous payoff functions. Reny's proof is purely existential, and is similar to a contradiction proof : it gives non hint of a method to compute a Nash equilibrium in the class of games considered. In this paper, we adapt the arguments of Reny in order to obtain, for better-reply-secure games : an elementary proof of Nash equilibria existence, which is a consequence of Kakutani's theorem, and a " constructive " proof, in the sense that we obtain Nash equilibria as limits of fixed-point of well chosen correspondences.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Université Panthéon-Sorbonne (Paris 1) in its series Cahiers de la Maison des Sciences Economiques with number b06001.
Length: 8 pages
Date of creation: Jan 2006
Date of revision:
Contact details of provider:
Postal: 106 - 112 boulevard de l'Hôpital, 75647 Paris cedex 13
Phone: 01 44 07 81 00
Fax: 01 44 07 81 09
Web page: http://mse.univ-paris1.fr/
More information through EDIRC
Reny's theorem; discontinuous payoffs.;
Find related papers by JEL classification:
- C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
This paper has been announced in the following NEP Reports:
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.:
- 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.
- Jean-Marc Bonnisseau & Pascal Gourdel & Hakim Hammami, 2005.
"Existence d'un équilibre de Nash dans un jeu discontinu,"
Cahiers de la Maison des Sciences Economiques
b05099, Université Panthéon-Sorbonne (Paris 1).
- Jean-Marc Bonnisseau & Pascal Gourdel & Hakim Hammami, 2005. "Existence d'un équilibre de Nash dans un jeu discontinu," UniversitÃ© Paris1 PanthÃ©on-Sorbonne (Post-Print and Working Papers) halshs-00173781, HAL.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Lucie Label).
If references are entirely missing, you can add them using this form.