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A fixed point theorem for discontinuous functions

Author

Listed:
  • Herings, P.J.J.

    (Tilburg University, School of Economics and Management)

  • van der Laan, G.
  • Talman, A.J.J.

    (Tilburg University, School of Economics and Management)

  • Yang, Z.F.

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.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Herings, P.J.J. & van der Laan, G. & Talman, A.J.J. & Yang, Z.F., 2008. "A fixed point theorem for discontinuous functions," Other publications TiSEM c0fd7fa8-2799-4aa7-9acd-6, Tilburg University, School of Economics and Management.
    • Handle: RePEc:tiu:tiutis:c0fd7fa8-2799-4aa7-9acd-635050e5a59f
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    File URL: https://pure.uvt.nl/ws/portalfiles/portal/924459/Talmanjan.pdf
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    References listed on IDEAS

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    2. Herings, P.J.J., 1995. "Static and dynamic aspects of general disequilibrium theory," Other publications TiSEM 489c698d-c257-47a3-90bd-3, Tilburg University, School of Economics and Management.
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    Citations

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    Cited by:

    1. Philippe Bich, 2007. "Nash equilibrium existence for some discontinuous games," Post-Print halshs-00188764, HAL.
    2. Philippe Bich, 2008. "An answer to a question of herings et al," Working Papers halshs-00265464, HAL.
    3. Philippe Bich, 2008. "An answer to a question of herings et al," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00265464, HAL.
    4. Zaifu Yang, 2008. "On the Solutions of Discrete Nonlinear Complementarity and Related Problems," Mathematics of Operations Research, INFORMS, vol. 33(4), pages 976-990, November.
    5. Philippe Bich, 2006. "Some fixed point theorems for discontinuous mappings," Cahiers de la Maison des Sciences Economiques b06066, Université Panthéon-Sorbonne (Paris 1).
    6. Philippe Bich, 2006. "Some fixed point theorems for discontinuous mappings," Post-Print halshs-00119033, HAL.
    7. Takao Fujimoto, 2013. "Fixed Point Theorems for Discontinuous Maps on a Non-convex Domain," Metroeconomica, Wiley Blackwell, vol. 64(3), pages 547-572, July.
    8. Philippe Bich, 2008. "An answer to a question of herings et al," Post-Print halshs-00287667, HAL.

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    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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