Probabilistic values on convex geometries

J.M. Bilbao, E. Lebrón and N. Jiménez

Annals of Operations Research, 1998, vol. 84, issue 0, 79-95

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

Date: 1998
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DOI: 10.1023/A:1018953323577

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