Table of Contents
ISRN Applied Mathematics
Volume 2011, Article ID 384625, 15 pages
Research Article

Equivalence between the Existence of an Approximate Equilibrium in a Competitive Economy and Sperner's Lemma: A Constructive Analysis

Faculty of Economics, Doshisha University, Kamigyo-ku, Kyoto 602-8580, Japan

Received 8 March 2011; Accepted 31 March 2011

Academic Editors: J. R. Fernandez and H.-T. Hu

Copyright © 2011 Yasuhito Tanaka. 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.

Linked References

  1. D. van Dalen, “Brouwer’s ε-fixed point from Sperner’s lemma,” Logic Group Preprint Series, vol. 275, pp. 1–20, 2009. View at Google Scholar
  2. W. Veldman, “Brouwer's approximate fixed-point theorem is equivalent to Brouwer's fan theorem,” in Logicism, intuitionism, and formalism, S. Lindström, E. Palmgren, K. Segerberg, and S. Hansen, Eds., vol. 341, pp. 277–299, Springer, Dordrecht, The Netherlands, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  3. E. Bishop and D. Bridges, Constructive Analysis, vol. 279, Springer, Berlin, Germany, 1985. View at Zentralblatt MATH
  4. D. Bridges and F. Richman, Varieties of Constructive Mathematics, vol. 97 of London Mathematical Society Lecture Note Series, Cambridge University Press, Cambridge, UK, 1987. View at Zentralblatt MATH
  5. D. S. Bridges and L. S. Vîţă, Techniques of Constructive Analysis, Springer, New York, NY, USA, 2006. View at Zentralblatt MATH
  6. F. E. Su, “Rental harmony: Sperner's lemma in fair division,” The American Mathematical Monthly, vol. 106, no. 10, pp. 930–942, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. Y. Tanaka, “A proof of the existence of an approximate Nash equilibrium in a finite strategic game directly by Sperner’s lemma: a constructive analysis,” Mimeograph. In press.
  8. J. Nash, “Non-cooperative games,” Annals of Mathematics, vol. 54, pp. 286–295, 1951. View at Publisher · View at Google Scholar · View at Zentralblatt MATH