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

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Date

2022-09

Authors

Sağlam, Çağrı

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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.

Source Title

Journal of Optimization Theory and Applications

Publisher

Springer

Keywords

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

Permalink

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

Published Version (Please cite this version)

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

Collections

Scholarly Publications - Economics

Language

English

Type