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A Probabilistic Representation of Exact Games on σ-Algebras

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Advances in Computational Intelligence (IPMU 2012)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 300))

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Abstract

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.

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Author information

Authors and Affiliations

  1. Faculty of Economics, Hosei University, 4342, Aihara, Machida, Tokyo, 194–0298, Japan

    Nobusumi Sagara

Authors
  1. Nobusumi Sagara
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Editor information

Editors and Affiliations

  1. Faculty of Economics, University of Catania, Corso Italia, 55, 95129, Catania, Italy

    Salvatore Greco  & Benedetto Matarazzo  & 

  2. CNRS UMR 7606, DAPA, LIP6 8, Université Pierre et Marie Curie - Paris6, rue du Capitaine Scott, F-75015, Paris, France

    Bernadette Bouchon-Meunier

  3. Dip. Matematica e Informatica, Università di Perugia, 06123, Perugia, Italy

    Giulianella Coletti

  4. Department of Computer and Management Science, University of Trento, Via Inama 5, 38122, Trento, Italy

    Mario Fedrizzi

  5. Machine Intelligence Institute — IONA College,, 10801, New Rochelle, NY, USA

    Ronald R. Yager

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© 2012 Springer-Verlag Berlin Heidelberg

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Sagara, N. (2012). A Probabilistic Representation of Exact Games on σ-Algebras. In: Greco, S., Bouchon-Meunier, B., Coletti, G., Fedrizzi, M., Matarazzo, B., Yager, R.R. (eds) Advances in Computational Intelligence. IPMU 2012. Communications in Computer and Information Science, vol 300. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31724-8_24

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  • DOI: https://doi.org/10.1007/978-3-642-31724-8_24

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31723-1

  • Online ISBN: 978-3-642-31724-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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