Proof of the Gale-Nikaido Lemma for sequentially locally non-constant multi-functions: A constructive analysis
Abstract
In this paper we constructively prove the Gale-Nikaido lemma for sequentially locally non-constant multi-functions (multi-valued functions or correspondences), which is the basis of a proof of the existence of an equilibrium in a competitive economy, and also we will show that our Gale-Nikaido lemma leads to Sperner's lemma. We follow the Bishop style constructive mathematics
Copyright © 2012 Yasuhito Tanaka. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Cite this article
Y. Tanaka, Proof of the Gale-Nikaido Lemma for sequentially locally non-constant multi-functions: A constructive analysis, J. Math. Comput. Sci. 2 (2012), 1743–1758.
BibTeX
@article{Tanaka2012,
author = {Tanaka, Yasuhito},
title = {Proof of the Gale-Nikaido Lemma for sequentially locally non-constant multi-functions: A constructive analysis},
journal = {J. Math. Comput. Sci.},
volume = {2},
year = {2012},
pages = {1743--1758},
doi = {}
}