A new class of convex games on sigma-algebras and the optimal partitioning of measurable spaces

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F11%3A10103327" target="_blank" >RIV/00216208:11320/11:10103327 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/s00182-010-0258-2" target="_blank" >http://dx.doi.org/10.1007/s00182-010-0258-2</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00182-010-0258-2" target="_blank" >10.1007/s00182-010-0258-2</a>

Result language
angličtina
Original language name
A new class of convex games on sigma-algebras and the optimal partitioning of measurable spaces
Original language description
We introduce ?-convexity, a new kind of game convexity defined on a ?-algebra of a nonatomic finite measure space. We show that ?-convex games are ?-average monotone. Moreover, we show that ?-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.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Publication year
2011
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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