A Probabilistic Representation of Exact Games on σ-Algebras

  • Nobusumi Sagara
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 300)


The 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.


Exact game Core Exact functional Choquet integral Law invariance Fatou property Anonymity P-convex measure 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Nobusumi Sagara
    • 1
  1. 1.Faculty of EconomicsHosei UniversityMachidaJapan

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