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