A direct proof of the Gale–Nikaido–Debreu lemma using Sperner’s lemma
Date
2022-09
Authors
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Source Title
Journal of Optimization Theory and Applications
Print ISSN
0022-3239
Electronic ISSN
Publisher
Springer
Volume
194
Issue
3
Pages
1072 - 1080
Language
English
Type
Article
Journal Title
Journal ISSN
Volume Title
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.
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Keywords
Fixed point theorem, Gale–Nikaido–Debreu lemma, General equilibrium, Simplex, Sperner lemma, Subdivision