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A Fixed Point Theorem for Discontinuous Functions

Author

Listed:
  • 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.)

Suggested Citation

  • Jean-Jacques Herings & Gerard van der Laan & Dolf Talman & Zaifu Yang, 2004. "A Fixed Point Theorem for Discontinuous Functions," Tinbergen Institute Discussion Papers 05-004/1, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20050004
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    Citations

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    Cited by:

    1. is not listed on IDEAS
    2. Philippe Bich, 2007. "Nash equilibrium existence for some discontinuous games," Post-Print halshs-00188764, HAL.
    3. Philippe Bich, 2008. "An answer to a question of herings et al," Working Papers halshs-00265464, HAL.
    4. Philippe Bich, 2008. "An answer to a question of herings et al," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00265464, HAL.
    5. 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.
    6. Philippe Bich, 2006. "Some fixed point theorems for discontinuous mappings," Cahiers de la Maison des Sciences Economiques b06066, Université Panthéon-Sorbonne (Paris 1).
    7. Philippe Bich, 2006. "Some fixed point theorems for discontinuous mappings," Post-Print halshs-00119033, HAL.
    8. Takao Fujimoto, 2013. "Fixed Point Theorems for Discontinuous Maps on a Non-convex Domain," Metroeconomica, Wiley Blackwell, vol. 64(3), pages 547-572, July.
    9. Philippe Bich, 2008. "An answer to a question of herings et al," Post-Print halshs-00287667, HAL.

    More about this item

    Keywords

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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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