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

Le, T.Le Van, C.Pham, N.-S.Sağlam, Çağrı2023-02-212023-02-212022-090022-3239http://hdl.handle.net/11693/111580The 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.EnglishFixed point theoremGale–Nikaido–Debreu lemmaGeneral equilibriumSimplexSperner lemmaSubdivisionA direct proof of the Gale–Nikaido–Debreu lemma using Sperner’s lemmaArticle10.1007/s10957-022-02067-2