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  • We introduce μ-convexity, a new kind of game convexity defined on a σ-algebra of a nonatomic finite measure space. We show that μ-convex games are μ-average monotone. Moreover, we show that μ-average monotone games are totally balanced and their core contains a nonatomic finite signed measure. We apply the results to the problem of partitioning a measurable space among a finite number of individuals. For this problem, we extend some results known for the case of individuals'' preferences that are representable by nonatomic probability measures to the more general case of nonadditive representations.
  • We introduce μ-convexity, a new kind of game convexity defined on a σ-algebra of a nonatomic finite measure space. We show that μ-convex games are μ-average monotone. Moreover, we show that μ-average monotone games are totally balanced and their core contains a nonatomic finite signed measure. We apply the results to the problem of partitioning a measurable space among a finite number of individuals. For this problem, we extend some results known for the case of individuals'' preferences that are representable by nonatomic probability measures to the more general case of nonadditive representations. (en)
Title
  • A new class of convex games on sigma-algebras and the optimal partitioning of measurable spaces
  • A new class of convex games on sigma-algebras and the optimal partitioning of measurable spaces (en)
skos:prefLabel
  • A new class of convex games on sigma-algebras and the optimal partitioning of measurable spaces
  • A new class of convex games on sigma-algebras and the optimal partitioning of measurable spaces (en)
skos:notation
  • RIV/00216208:11320/11:10103327!RIV12-MSM-11320___
http://linked.open...avai/riv/aktivita
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  • Z(MSM0021620838)
http://linked.open...iv/cisloPeriodika
  • 3
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  • 183935
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  • RIV/00216208:11320/11:10103327
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  • fair division; convex game; nonatomic finite measure (en)
http://linked.open.../riv/klicoveSlovo
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  • DE - Spolková republika Německo
http://linked.open...ontrolniKodProRIV
  • [C1E19493D41E]
http://linked.open...i/riv/nazevZdroje
  • International Journal of Game Theory
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http://linked.open...v/svazekPeriodika
  • 40
http://linked.open...iv/tvurceVysledku
  • Vlach, Milan
  • sagara, Nobusumi
http://linked.open...ain/vavai/riv/wos
  • 000293475300010
http://linked.open...n/vavai/riv/zamer
issn
  • 0020-7276
number of pages
http://bibframe.org/vocab/doi
  • 10.1007/s00182-010-0258-2
http://localhost/t...ganizacniJednotka
  • 11320
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