Geodesic
An existence result on partitioning of a measurable space: Pareto optimality and core
Kybernetika, Tome 42 (2006) no. 4, pp. 475-481.

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This paper investigates the problem of optimal partitioning of a measurable space among a finite number of individuals. We demonstrate the 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.
Classification : 28A10, 28B05, 90C29, 91B32
Keywords: optimal partitioning; nonatomic finite measure; nonadditive set function; Pareto optimality; core 
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     author = {Sagara, Nobusumi},
     title = {An existence result on partitioning of a measurable space: {Pareto} optimality and core},
     journal = {Kybernetika},
     pages = {475--481},
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     volume = {42},
     number = {4},
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     zbl = {1249.90241},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2006__42_4_a6/}
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Sagara, Nobusumi. An existence result on partitioning of a measurable space: Pareto optimality and core. Kybernetika, Tome 42 (2006) no. 4, pp. 475-481. http://geodesic.mathdoc.fr/item/KYB_2006__42_4_a6/