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Axiomatic characterizations of probabilistic and cardinal-probabilistic interaction indices

By Katsushige Fujimoto, Ivan Kojadinovic and Jean-Luc Marichal

Abstract

In the framework of cooperative game theory, the concept of interaction index, which can be regarded as an extension of that of value, has been recently proposed to measure the interaction phenomena among players. Axiomatizations of two classes of interaction indices, namely probabilistic interaction indices and cardinal-probabilistic interaction indices, generalizing probabilistic values and semivalues, respectively, are first proposed. The axioms we utilize are based on natural generalizations of axioms involved in the axiomatizations of values. In the second half of the paper, existing instances of cardinal-probabilistic interaction indices encountered thus far in the literature are also axiomatized

Topics: cooperative games, interaction among players, values and interaction indices, Physical, chemical, mathematical & earth Sciences :: Mathematics [G03], Physique, chimie, mathématiques & sciences de la terre :: Mathématiques [G03], Business & economic sciences :: Quantitative methods in economics & management [B09], Sciences économiques & de gestion :: Méthodes quantitatives en économie & gestion [B09]
Year: 2006
DOI identifier: 10.1016/j.geb.2005.03.002
OAI identifier: oai:orbilu.uni.lu:10993/2839
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