Direct Proofs of the Existence of Equilibrium, the Gale-Nikaido-Debreu Lemma and the Fixed Point Theorems using Sperner’s Lemma

Thanh Le, Cuong Le Van, Ngoc-Sang Pham and Çağrı Sağlam

MPRA Paper from University Library of Munich, Germany

Abstract: In this paper, we use Sperner’s lemma to prove the existence of general equilibrium for a competitive economy with production or with uncertainty and financial assets. We then show that the direct use of Sperner’s lemma together with Carathéodory’s convexity theorem and basic properties of topology such as partition of unit, finite covering of a compact set allow us to bypass the Kakutani fixed point theorem even in establishing the Gale-Nikaido-Debreu Lemma. We also provide a new proof of the Kakutani fixed point theorem based on Sperner’s lemma.

Keywords: Sperner lemma; Simplex; Subdivision; Fixed Point Theorem; Gale-Nikaido-Debreu Lemma; General Equilibrium. (search for similar items in EconPapers)
JEL-codes: C60 C62 D5 (search for similar items in EconPapers)
Date: 2020-05-03, Revised 2020-10-28
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://mpra.ub.uni-muenchen.de/110933/1/MPRA_paper_110933.pdf original version (application/pdf)

Related works:
Working Paper: Direct Proofs of the Existence of Equilibrium, the Gale-Nikaido-Debreu Lemma and the Fixed Point Theorems using Sperner's Lemma (2021)
Working Paper: Direct Proofs of the Existence of Equilibrium, the Gale-Nikaido-Debreu Lemma and the Fixed Point Theorems using Sperner's Lemma (2021)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:pra:mprapa:110933

Access Statistics for this paper

More papers in MPRA Paper from University Library of Munich, Germany Ludwigstraße 33, D-80539 Munich, Germany. Contact information at EDIRC.
Bibliographic data for series maintained by Joachim Winter ().