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

Marco Dall'AGLIO, Camilla Di LUCA, Lucia MILONE
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
more » ... inner procedure by Brams and Taylor to the three-player case, without the guarantee of envy-freeness.
doi:10.5277/ord170303 fatcat:3al5cf33w5fxxdxi5hpad5d5su