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Finding the Pareto optimal equitable allocation of homogeneous divisible goods among three players

Dall'Aglio M., Di Luca C., Milone L.

Operations Research and Decisions

2017

Vol. 27, No. 3

35--50

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.