A Direct Proof of the Gale-Nikaido-Debreu Lemma Using Sperner's Lemma

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.

Automated summary

This paper proves the Gale-Nikaido-Debreu lemma using Sperner's lemma and basic elements of topology, which plays an important role in establishing the existence of competitive equilibrium.