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Two lemmas that changed general equilibrium theory

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Abstract

This short paper, published in Games and Economic Behavior (July 2009) "In Memoriam" of David Gale, emphasizes the seminal role played by two lemmas of David Gale in the development of the foundations of General Equilibrium Theory

Suggested Citation

  • Monique Florenzano, 2009. "Two lemmas that changed general equilibrium theory," Documents de travail du Centre d'Economie de la Sorbonne 09052, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    • Handle: RePEc:mse:cesdoc:09052
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    File URL: ftp://mse.univ-paris1.fr/pub/mse/CES2009/09052.pdf
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    References listed on IDEAS

    as
    1. Gale, D. & Mas-Colell, A., 1979. "Corrections to an equilibrium existence theorem for a general model without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 6(3), pages 297-298, December.
    2. Gale, David, 1973. "Pure exchange equilibrium of dynamic economic models," Journal of Economic Theory, Elsevier, vol. 6(1), pages 12-36, February.
    3. Gerard Debreu, 1956. "Market Equilibrium," Cowles Foundation Discussion Papers 10, Cowles Foundation for Research in Economics, Yale University.
    4. Mas-Colell, Andrew, 1974. "An equilibrium existence theorem without complete or transitive preferences," Journal of Mathematical Economics, Elsevier, vol. 1(3), pages 237-246, December.
    5. Geistdoerfer-Florenzano, Monique, 1982. "The gale-nikaido-debreu lemma and the existence of transitive equilibrium with or without the free-disposal assumption," Journal of Mathematical Economics, Elsevier, vol. 9(1-2), pages 113-134, January.
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    Cited by:

    1. Le, Thanh & Le Van, Cuong & Pham, Ngoc-Sang & Sağlam, Çağrı, 2020. "Direct Proofs of the Existence of Equilibrium, the Gale-Nikaido-Debreu Lemma and the Fixed Point Theorems using Sperner’s Lemma," MPRA Paper 110933, University Library of Munich, Germany, revised 28 Oct 2020.
    2. M. Ali Khan & Richard P. McLean & Metin Uyanik, 2025. "Alternative proofs of the GNKD and KKMS lemmas: a game-theoretic underpinning," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 13(1), pages 1-20, April.
    3. Thanh Le & Cuong Le Van & Ngoc-Sang Pham & Cagri Saglam, 2022. "A Direct Proof of the Gale–Nikaido–Debreu Lemma Using Sperner’s Lemma," Journal of Optimization Theory and Applications, Springer, vol. 194(3), pages 1072-1080, September.
    4. Le, Thanh & Le Van, Cuong & Pham, Ngoc-Sang & Sağlam, Çağrı, 2020. "Sperner Lemma, Fixed Point Theorems, and the Existence of Equilibrium," MPRA Paper 100084, University Library of Munich, Germany.

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    Keywords

    Fixed points; equilibrium; excess demand correspondence; Gale-Nikaido-Debreu lemma; simultaneous optimization approach; Michael selection theorems;
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