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

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

Journal of Optimization Theory and Applications（2022）

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摘要

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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关键词

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

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