Characterizing and Finding the Pareto Optimal Equitable Allocation of Homogeneous Divisible Goods Among Three Players

TL;DR

This paper characterizes Pareto optimal equitable allocations for dividing homogeneous divisible goods among three players, introducing two algorithms based on geometric objects to find such allocations efficiently.

Contribution

It provides a novel characterization of optimal allocations and develops two exact algorithms leveraging geometric relationships in fair division.

Findings

Characterization of Pareto optimal equitable allocations

Development of two exact algorithms for allocation search

Use of geometric objects IPS and RNS in fair division

Abstract

We consider the division of a finite number of homogeneous divisible items among three players. Under the assumption that each player assigns a positive value to every item, we characterize the optimal allocations and we develop two exact algorithms for its search. Both the characterization and the algorithm are based on the tight relationship two geometric objects of fair division: the Individual Pieces Set (IPS) and the Radon-Nykodim Set (RNS).