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

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.

Sperner’s lemma and competitive equilibrium with incomplete financial markets

“…2 In a companion paper (Le, Le Van, Pham and Saglam, 2022), we use Sperner's lemma to prove the Gale-Nikaido-Debreu lemma.…”