Sperner Lemma, Fixed Point Theorems, and the Existence of Equilibrium

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

MPRA Paper from University Library of Munich, Germany

Abstract: In characterizing the existence of general equilibrium, existing studies mainly draw on Brouwer and Kakutani fixed point theorems and, to some extent, Gale-Nikaido-Debreu lemma. In this paper, we show that Sperner lemma can play a role as an alternative powerful tool for the same purpose. Specifically, Sperner lemma can be used to prove those theorems as well as the lemma. Additionally, Kakutani theorem is shown as a corollary of Gale-Nikaido-Debreu lemma. For a demonstration of the use of Sperner lemma to prove general equilibrium existence, we consider two competitive economies marked either by production goods or financial assets. In each case, we successfully provide another proof on the existence of a general equilibrium using only Sperner lemma and without a need to call on the fixed point theorems or the 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
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/100084/1/MPRA_paper_100084.pdf original version (application/pdf)
https://mpra.ub.uni-muenchen.de/103832/12/MPRA_paper_103832.pdf revised version (application/pdf)

Related works:
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:100084

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 ().