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 procedureby Brams and Taylor to the three-player case, without the guarantee of envy-freeness.

Finding the Pareto Optimal Equitable Allocation of Homogeneous Divisible Goods Among Three Players / Dall'Aglio, Marco; DI LUCA, Camilla; Milone, Lucia. - In: OPERATIONS RESEARCH AND DECISIONS. - ISSN 2081-8858. - 27:3(2017), pp. 35-50. [10.5277/ord170303]

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

Marco Dall'aglio
;
Camilla Di Luca;Lucia Milone
2017

Abstract

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 procedureby Brams and Taylor to the three-player case, without the guarantee of envy-freeness.
fair division, Pareto optimality, raph theory, adjusted winner procedure
Finding the Pareto Optimal Equitable Allocation of Homogeneous Divisible Goods Among Three Players / Dall'Aglio, Marco; DI LUCA, Camilla; Milone, Lucia. - In: OPERATIONS RESEARCH AND DECISIONS. - ISSN 2081-8858. - 27:3(2017), pp. 35-50. [10.5277/ord170303]
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11385/176581
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