An existence result on partitioning of a measurable space: Pareto optimality and core. (English) Zbl 1249.90241

Summary: The author investigates the problem of optimal partitioning of a measurable space into a finite number of individuals. We demonstrate sufficient conditions for the existence of weakly Pareto optimal partitions and for the equivalence between weak Pareto optimality and Pareto optimality. We demonstrate that every weakly Pareto optimal partition is a solution to the problem of maximizing a weighted sum of individual utilities. We also provide sufficient conditions for the existence of core partitions with non-transferable and transferable utility.


90C29 Multi-objective and goal programming
28A10 Real- or complex-valued set functions
28B05 Vector-valued set functions, measures and integrals
91B32 Resource and cost allocation (including fair division, apportionment, etc.)
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