Skip to content


  • Research Article
  • Open Access

Fixed points as Nash equilibria

Fixed Point Theory and Applications20062006:36135

  • Received: 27 March 2006
  • Accepted: 1 October 2006
  • Published:


The existence of fixed points for single or multivalued mappings is obtained as a corollary of Nash equilibrium existence in finitely many players games.


  • Nash Equilibrium
  • Differential Geometry
  • Computational Biology
  • Multivalued Mapping
  • Player Game


Authors’ Affiliations

Department of Economics, Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Marquês de São Vicente 225, Rio de Janeiro, 22453-900, Brazil


  1. Brouwer LEJ: Über Abbildung von Mannigfaltigkeiten. Mathematische Annalen 1912,71(4):598.MATHGoogle Scholar
  2. Kakutani S: A generalization of Brouwer's fixed point theorem. Duke Mathematical Journal 1941,8(3):457–459. 10.1215/S0012-7094-41-00838-4MathSciNetView ArticleMATHGoogle Scholar
  3. Nash JF: Equilibrium points in n-person games. Proceedings of the National Academy of Sciences of the United States of America 1950,36(1):48–49. 10.1073/pnas.36.1.48MathSciNetView ArticleMATHGoogle Scholar
  4. Nash JF: Non-cooperative games. Annals of Mathematics. Second Series 1951, 54: 286–295. 10.2307/1969529MathSciNetView ArticleMATHGoogle Scholar
  5. Zhao J: The equivalence between four economic theorems and Brouwer's fixed point theorem. In Working Paper. Departament of Economics, Iowa State University, Iowa; 2002.Google Scholar


© Juan Pablo Torres-Martínez. 2006

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.