Characterizing and Finding the Pareto Optimal Equitable Allocation of   Homogeneous Divisible Goods Among Three Players
  We consider the division 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 characterize the optimal allocations and we develop two exact algorithms for its search. Both the characterization and the algorithm are based on the tight relationship two geometric objects of fair division: the Individual Pieces Set (IPS) and the Radon-Nykodim Set (RNS). 
Marco Dall'Aglio, Camilla Di Luca and Lucia Milone
math.OC cs.GT