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\iteman{io-port 06112036}
\itemau{Sagara, Nobusumi}
\itemti{A probabilistic representation of exact games on $\sigma $-algebras.}
\itemso{Greco, Salvatore (ed.) et al., Advances in computational intelligence. 14th international conference on information processing and management of uncertainty in knowledge-based systems, IPMU 2012, Catania, Italy, July 9--13, 2012. Proceedings, Part IV. Berlin: Springer (ISBN 978-3-642-31723-1/pbk; 978-3-642-31724-8/ebook). Communications in Computer and Information Science 300, 228-237 (2012).}
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Summary: The purpose of this paper is to establish the intrinsic relations between the cores of exact games on $\sigma$-algebras and the extensions of exact games to function spaces. Given a probability space, to derive a probabilistic representation for exact functionals, we endow them with two probabilistic conditions: law invariance and the Fatou property. The representation theorem for exact functionals lays a probabilistic foundation for nonatomic scalar measure games. Based on the notion of $P$-convexity, we also investigate the equivalent conditions for the representation of anonymous convex games.
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\itemli{doi:10.1007/978-3-642-31724-8\_24}
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