Decomposition of interaction indices: alternative interpretations of cardinal-probabilistic interaction indices

Sébastien Courtin (), Rodrigue Tido Takeng and Frédéric Chantreuil ()
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Sébastien Courtin: IDEES - Identité et Différenciation de l’Espace, de l’Environnement et des Sociétés - UNICAEN - Université de Caen Normandie - NU - Normandie Université - ULH - Université Le Havre Normandie - NU - Normandie Université - UNIROUEN - Université de Rouen Normandie - NU - Normandie Université - CNRS - Centre National de la Recherche Scientifique - IRIHS - Institut de Recherche Interdisciplinaire Homme et Société - UNIROUEN - Université de Rouen Normandie - NU - Normandie Université, UNICAEN - Université de Caen Normandie - NU - Normandie Université
Rodrigue Tido Takeng: CREM - Centre de recherche en économie et management - UNICAEN - Université de Caen Normandie - NU - Normandie Université - UR - Université de Rennes - CNRS - Centre National de la Recherche Scientifique
Frédéric Chantreuil: CEMOI - Centre d'Économie et de Management de l'Océan Indien - UR - Université de La Réunion

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Abstract: In cooperative game theory, the concept of interaction index is an extension of the concept of value, considering interaction among players. In this paper we focus on cardinal-probabilistic interaction indices which are generalizations of the class of semivalues. We provide two types of decompositions. With the first one, a cardinal-probabilistic interaction index for a given coalition equals the difference between its external interaction index (or co-Möbius transfom) and a weighted sum of the individual impact of the remaining players on the interaction index of the considered coalition. The second decomposition, based on the notion of the "decomposer", splits an interaction index into a direct part, the decomposer, which measures the interaction in the coalition considered, and an indirect part, which indicates how all remaining players individually affect the interaction of the coalition considered. We propose alternative characterization of the cardinal-probabilistic interaction indices. We then propose an illustration with a well-known example in Multicriteria Aid for Decisions.

Keywords: Game theory; Multicriteria Aid for Decisions; Cardinal-probabilistic interaction indices; External interaction index JEL Codes: C71 (search for similar items in EconPapers)
Date: 2020-08-22
New Economics Papers: this item is included in nep-cdm, nep-gth and nep-ore
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