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The Gale–Nikaido–Debreu lemma with discontinuous excess demand

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  • Bernard Cornet

    (University of Kansas)

Abstract

We provide a generalization of the Gale–Nikaido–Debreu’s lemma for discontinuous excess demand in the light of recent work on the existence of equilibria in games with discontinuous payoffs. The standard upper hemicontinuity property of the excess demand is replaced by the weaker concept of “continuous inclusion property” introduced by He and Yannelis (J Math Anal Appl 450(2):1421–1433, 2017) and we allow for the cone P of admissible prices to be general enough to cover cases for which commodities cannot be freely disposed of.

Suggested Citation

  • Bernard Cornet, 2020. "The Gale–Nikaido–Debreu lemma with discontinuous excess demand," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(2), pages 169-180, October.
    • Handle: RePEc:spr:etbull:v:8:y:2020:i:2:d:10.1007_s40505-019-00181-5
    DOI: 10.1007/s40505-019-00181-5
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    References listed on IDEAS

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    1. Philip J. Reny, 2016. "Equilibrium in discontinuous games without complete or transitive preferences," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(1), pages 1-4, April.
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    3. Guoqiang Tian, 2016. "On the existence of price equilibrium in economies with excess demand functions," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(1), pages 5-16, April.
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    Cited by:

    1. Gourdel, Pascal & Le Van, Cuong & Pham, Ngoc-Sang & Tran Viet, Cuong, 2023. "Hartman-Stampacchia theorem, Gale-Nikaido-Debreu lemma, and Brouwer and Kakutani fixed-point theorems," MPRA Paper 116541, University Library of Munich, Germany.

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    More about this item

    Keywords

    Existence of equilibrium; Debreu–Gale–Nikaido’s lemma; Fixed-point;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General
    • D53 - Microeconomics - - General Equilibrium and Disequilibrium - - - Financial Markets

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