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


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2022-07-14

AUTHORS

Thanh Le, Cuong Le Van, Ngoc-Sang Pham, Cagri Saglam

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.

PAGES

1072-1080

References to SciGraph publications

  • 1928-12. Neuer beweis für die invarianz der dimensionszahl und des gebietes in ABHANDLUNGEN AUS DEM MATHEMATISCHEN SEMINAR DER UNIVERSITÄT HAMBURG
  • 2001. Finite Dimensional Convexity and Optimization in NONE
  • 2009-12. General equilibrium and fixed point theory: A partial survey in JOURNAL OF FIXED POINT THEORY AND APPLICATIONS
  • 2003. General Equilibrium Analysis, Existence and Optimality Properties of Equilibria in NONE
  • 1982-07. Topological degree and the Sperner lemma in JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • 1907-03. Über den Variabilitätsbereich der Koeffizienten von Potenzreihen, die gegebene Werte nicht annehmen in MATHEMATISCHE ANNALEN
  • 1911-03. Über Abbildung von Mannigfaltigkeiten in MATHEMATISCHE ANNALEN
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    http://scigraph.springernature.com/pub.10.1007/s10957-022-02067-2

    DOI

    http://dx.doi.org/10.1007/s10957-022-02067-2

    DIMENSIONS

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