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

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A_direct_proof_of_the_Gale–Nikaido–Debreu_lemma_using_Sperner’s_lemma.pdf (208.05 KB)

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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Article

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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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Fixed point theorem, Gale–Nikaido–Debreu lemma, General equilibrium, Simplex, Sperner lemma, Subdivision

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http://hdl.handle.net/11693/111580

Published Version (Please cite this version)

https://doi.org/https://doi.org/10.1007/s10957-022-02067-2

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Scholarly Publications - Economics