A Direct Proof of the Gale–Nikaido–Debreu Lemma Using Sperner’s Lemma

Thanh Le, Cuong Le Van (), Ngoc-Sang Pham and Çağrı Sağlam
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Cuong Le Van: PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, IPAG Business School, TIMAS - Institute of Mathematics and Applied Science

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Abstract: The Gale–Nikaido–Debreu lemma plays an important role in establishing the existence of competitive equilibrium. In this paper, we use Sperner's lemma and basic elements of topology to prove the Gale–Nikaido–Debreu lemma.

Keywords: Sperner lemma; Simplex; Subdivision; Fixed point theorem; Gale–Nikaido–Debreu lemma; General equilibrium (search for similar items in EconPapers)
Date: 2022-09
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Citations: View citations in EconPapers (4)

Published in Journal of Optimization Theory and Applications, 2022, 194 (3), pp.1072-1080. ⟨10.1007/s10957-022-02067-2⟩

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Related works:
Journal Article: A Direct Proof of the Gale–Nikaido–Debreu Lemma Using Sperner’s Lemma (2022)
Working Paper: A Direct Proof of the Gale–Nikaido–Debreu Lemma Using Sperner’s Lemma (2022)
Working Paper: A Direct Proof of the Gale–Nikaido–Debreu Lemma Using Sperner’s Lemma (2022)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-03960256

DOI: 10.1007/s10957-022-02067-2

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