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An existence result on partitioning of a measurable space: Pareto optimality and core
Kybernetika, Tome 42 (2006) no. 4, pp. 475-481 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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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     title = {An existence result on partitioning of a measurable space: {Pareto} optimality and core},
     journal = {Kybernetika},
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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/

[1] Barbanel J. B., Zwicker W. S.: Two applications of a theorem of Dvoretsky, Wald, and Wolfovitz to cake division. Theory and Decision 43 (1997), 203–207 | DOI | MR

[2] Bondareva O. N.: Some applications of linear programming methods to the theory of cooperative games (in Russian). Problemy Kibernet. 10 (1963), 119–139 | MR

[3] Dubins L. E., Spanier E. H.: How to cut a cake fairly. Amer. Math. Monthly 68 (1961), 1–17 | DOI | MR | Zbl

[4] Legut J.: Market games with a continuum of indivisible commodities. Internat. J. Game Theory 15 (1986), 1–7 | DOI | MR | Zbl

[5] Sagara N.: An Existence Result on Partitioning of a Measurable Space: Equity and Efficiency. Faculty of Economics, Hosei University 2006, mimeo

[6] Sagara N., Vlach M.: Representation of Convex Preferences in a Nonatomic Measure Space: $\varepsilon $-Pareto Optimality and $\varepsilon $-Core in Cake Division. Faculty of Economics, Hosei University 2006, mimeo

[7] Scarf H. E.: The core of an $N$ person game. Econometrica 35 (1967), 50–69 | DOI | MR | Zbl

[8] Shapley L.: On balanced sets and cores. Naval Res. Logist. 14 (1967), 453–460 | DOI