Existence of a simple and equitable fair division: a short proof

TL;DR

This paper presents a concise proof demonstrating that a simple and equitable division of a good among multiple players always exists, contributing to fair division theory.

Contribution

It provides a short, elegant proof confirming the existence of equitable divisions, simplifying previous approaches.

Findings

Existence of equitable division proven

Short proof enhances understanding

Applicable to any number of players

Abstract

In this note we study how to share a good between n players in a simple and equitable way. We give a short proof for the existence of such fair divisions.