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: IPAG Business School, Paris School of Economics TIMAS

Journal of Optimization Theory and Applications, 2022, vol. 194, issue 3, No 13, 1072-1080

Abstract: 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
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Citations: View citations in EconPapers (4)

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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)
Working Paper: A Direct Proof of the Gale–Nikaido–Debreu Lemma Using Sperner’s Lemma (2022)
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DOI: 10.1007/s10957-022-02067-2

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