Axiomatic characterizations of generalized values

Authors:
Jean-Luc Marichal;Ivan Kojadinovic;Katsushige Fujimoto
Affiliations:
Applied Mathematics Unit, University of Luxembourg, Luxembourg, Luxembourg;LINA CNRS FRE, Site École Polytechnique de l'Université de Nantes, Rue Christian Pauc, Nantes, France;Faculty of Economics, Fukushima University, Kanayagawa, Fukushima, Japan
Venue:
Discrete Applied Mathematics
Year:
2007

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Abstract

In the framework of cooperative game theory, the concept of generalized value, which is an extension of that of value, has been recently proposed to measure the overall influence of coalitions in games. Axiomatizations of two classes of generalized values, namely probabilistic generalized values and generalized semivalues, which extend probabilistic values and semivalues, respectively, are first proposed. The axioms we utilize are based on natural extensions of axioms involved in the axiomatizations of values. In the second half of the paper, special instances of generalized semivalues are also axiomatized.