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Cores and Stable Sets of Finite Dimensional Games
, 2003
"... In this paper we study exact TU games having Þnite dimensional non-atomic cores, a class of games that includes relevant economic games. We Þrst characterize them by showing that they are a particular type of market games. Using this characterization, we then show that in such a class the cores are ..."
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In this paper we study exact TU games having Þnite dimensional non-atomic cores, a class of games that includes relevant economic games. We Þrst characterize them by showing that they are a particular type of market games. Using this characterization, we then show that in such a class the cores are their unique von Neumann-Morgenstern stable sets.
A New Class of Convex Games on σ-Algebras and the Optimal Partitioning of Measurable Spaces∗
, 2009
"... uate Studies for Informatics. †Corresponding author. 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-av-erage monotone games are totally balanced and their ..."
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uate Studies for Informatics. †Corresponding author. 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-av-erage 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 individ-uals. For this problem, we extend some results known for the case of individuals ’ preferences that are representable by nonatomic probabil-ity measures to the more general case of nonadditive representations.
