Constructive proof of the existence of equilibrium in competitive economy with sequentially locally non-constant excess demand functions

TL;DR

This paper provides a constructive proof for the existence of equilibrium in a competitive economy with specific excess demand functions, establishing a link to Sperner's lemma and fixed point theorems.

Contribution

It introduces a constructive proof for equilibrium existence under sequentially locally non-constant excess demand functions, connecting economic equilibrium to Sperner's lemma.

Findings

Equilibrium existence is equivalent to Sperner's lemma.

Constructive proof based on fixed point approximation.

Links economic equilibrium to combinatorial topology.

Abstract

We present a constructive proof of the existence of an equilibrium in a competitive economy with sequentially locally non-constant excess demand functions. And we will show that the existence of such an equilibrium implies Sperner's lemma. Since the existence of an equilibrium is derived from the existence an approximate fixed point of uniformly continuous functions, which is derived from Sperner's lemma, the existence of an equilibrium in a competitive economy with sequentially locally non-constant excess demand functions is equivalent to Sperner's lemma.