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Probabilistic values on convex geometries

Author

Listed:
  • J.M. Bilbao
  • E. Lebrón
  • N. Jiménez

Abstract

A game on a convex geometry is a real-valued function defined on the family L of the closed sets of a closure operator which satisfies the finite Minkowski-Krein-Milmanproperty. If L is the Boolean algebra 2 N , then we obtain an n-person cooperative game. We will extend the work of Weber on probabilistic values to games on convex geometries. As a result, we obtain a family of axioms that give rise to several probabilistic values and a unique Shapley value for games on convex geometries. Copyright Kluwer Academic Publishers 1998

Suggested Citation

  • J.M. Bilbao & E. Lebrón & N. Jiménez, 1998. "Probabilistic values on convex geometries," Annals of Operations Research, Springer, vol. 84(0), pages 79-95, December.
    • Handle: RePEc:spr:annopr:v:84:y:1998:i:0:p:79-95:10.1023/a:1018953323577
    DOI: 10.1023/A:1018953323577
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    Cited by:

    1. Michel Grabisch, 2011. "Ensuring the boundedness of the core of games with restricted cooperation," Annals of Operations Research, Springer, vol. 191(1), pages 137-154, November.
    2. Michel Grabisch & Peter Sudhölter, 2014. "The positive core for games with precedence constraints," Documents de travail du Centre d'Economie de la Sorbonne 14036, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    3. Rene van den Brink & Ilya Katsev & Gerard van der Laan, 2023. "Properties of Solutions for Games on Union-Closed Systems," Mathematics, MDPI, vol. 11(4), pages 1-16, February.

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