Issue: 2017/Vol.27/No.3, Pages 35-50
FINDING THE PARETO OPTIMAL EQUITABLE ALLOCATION OF HOMOGENEOUS DIVISIBLE GOODS AMONG THREE PLAYERS
Cite as: M. Dall'Aglio, C. D. Luca, L. Milone. Finding the Pareto optimal equitable allocation of homogeneous divisible goods among three players. Operations Research and Decisions 2017: 27(3), 35-50. DOI 10.5277/ord170303
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.
Keywords: fair division, Pareto optimality, graph theory, adjusted winner procedure
Received: 12 September 2017 Accepted: 5 November 2017