Abstract
AbstractThe purpose of this paper is to establish the intrinsic relations between the cores of exact games on σ-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.KeywordsExact gameCoreExact functionalChoquet integralLaw invarianceFatou propertyAnonymity P-convex measure
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