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Une note sur un théorème de point-fixe

Author

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  • Pascal Gourdel

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

Abstract

We present a theorem on the existence of a maximal element for a correspondence which is upper hemi-continuous in some variables and which satisfies with respect to the other ones one the following conditions: (i) lower semi-continuous if the space has a finite dimension, (ii) lower semi-continuous if the space is complete, (iii) open fibers. This theorem generalizes the result of Gale and Mas-Colell (1975-1979) and the one of Bergstrom (1975) and extend to the infinite dimensional setting the result of Gourdel (1995).

Suggested Citation

  • Pascal Gourdel, 2006. "Une note sur un théorème de point-fixe," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00118919, HAL.
    • Handle: RePEc:hal:cesptp:halshs-00118919
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00118919
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    Keywords

    upper hemi-continuous; maximal element; fixed-point; selection theorems; endogenous endowments; théorèmes de sélection; hémi-continuité supérieure; élément maximal; Point-fixe;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General

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