A direct proof of the Gale–Nikaido–Debreu lemma using Sperner’s lemma

Date
2022-09
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Source Title
Journal of Optimization Theory and Applications
Print ISSN
0022-3239
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Publisher
Springer
Volume
194
Issue
3
Pages
1072 - 1080
Language
English
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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.

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