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A Fixed Point Theorem for Discontinuous Functions

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Author Info

  • Jean-Jacques Herings

    ()
    (Maastricht University)

  • Gerard van der Laan

    ()
    (Faculty of Economics and Business Administration, Vrije Universiteit Amsterdam)

  • Dolf Talman

    ()
    (Tilburg University)

  • Zaifu Yang

    ()
    (Yokohama National University)

Abstract

Any function from a non-empty polytope into itself that is locally gross direction preserving is shown to have the fixed point property. Brouwer's fixed point theorem for continuous functions is a special case. We discuss the application of the result in the area of non-cooperative game theory. This discussion paper has resulted in a publication in Operations Research Letters . (2008, vol. 36, issue 1, pp.89-93.)

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Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 05-004/1.

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Date of creation: 11 Jan 2004
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Handle: RePEc:dgr:uvatin:20050004

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Related research

Keywords: Fixed point; simplicial subdivision; discontinuity; equilibrium;

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References

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  1. P. Jean-Jacques Herings, 2000. "Two simple proofs of the feasibility of the linear tracing procedure," Economic Theory, Springer, vol. 15(2), pages 485-490.
  2. Shoven,John B. & Whalley,John, 1992. "Applying General Equilibrium," Cambridge Books, Cambridge University Press, number 9780521319867.
  3. 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.
  4. Carolyn Pitchik, 1981. "Equilibria of a Two-Person Non-Zero Sum Noisy Game of Timing," Cowles Foundation Discussion Papers 579, Cowles Foundation for Research in Economics, Yale University.
  5. Talman, A.J.J. & Yamamoto, Y., 1989. "A simplicial algorithm for stationary point problems on polytopes," Open Access publications from Tilburg University urn:nbn:nl:ui:12-153111, Tilburg University.
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Cited by:
  1. Philippe Bich, 2008. "An answer to a question of herings et al," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00265464, HAL.
  2. Philippe Bich, 2006. "Some fixed point theorems for discontinuous mappings," Cahiers de la Maison des Sciences Economiques b06066, Université Panthéon-Sorbonne (Paris 1).

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