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Nash and Walras Equilibrium

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Abstract

The existence of Nash and Walras equilibrium is proved via Brouwer's Fixed Point Theorem, without recourse to Kakutani's Fixed Point Theorem for correspondences. The domain of the Walras fixed point map is confined to the price simplex, even when there is production and weakly quasi-convex preferences. The key idea is to replace optimization with "satisficing improvement," i.e., to replace the Maximum Principle with the "Satisficing Principle."

Suggested Citation

  • John Geanakoplos, 1996. "Nash and Walras Equilibrium," Cowles Foundation Discussion Papers 1131R3, Cowles Foundation for Research in Economics, Yale University, revised Feb 2002.
    • Handle: RePEc:cwl:cwldpp:1131r3
    Note: CFP 1058
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    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d11/d1131-r3.pdf
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    More about this item

    Keywords

    Equilibrium; Nash; Walras; Brouwer; Kakutani;
    All these keywords.

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium

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