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

We consider the allocation 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 develop a simple algorithm that returns a Pareto optimal and equitable allocation. This is based on the tight relationshi...

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Bibliographic Details
Published in:Operations research and decisions 2017-01, Vol.27 (no. 3), p.35-50
Main Authors: Marco Dall'Aglio, Camilla Di Luca, Lucia Milone
Format: Article
Language:English
Online Access:Get full text
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Summary:We consider the allocation 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 develop a simple algorithm that returns a Pareto optimal and equitable allocation. This is based on the tight relationship between two geometric objects of fair division: The Individual Pieces Set (IPS) and the Radon-Nykodim Set (RNS). The algorithm can be considered as an extension of the Adjusted Winner procedure by Brams and Taylor to the three-player case, without the guarantee of envy-freeness. (original abstract)
ISSN:2081-8858
2391-6060
DOI:10.5277/ord170303