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We consider the division of a finite number of homogeneous divisible itemsamong three players. Under the assumption that each player assigns a positivevalue to every item, we characterize the optimal allocations and we develop twoexact algorithms for its search. Both the characterization and the algorithmare based on the tight relationship two geometric objects of fair division: theIndividual Pieces Set (IPS) and the Radon-Nykodim Set (RNS).

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