"A Direct Proof of the Gale–Nikaido–Debreu Lemma Using Sperner's Lemma" by Thanh Le, Cuong Le Van et al.
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: uow.edu.au