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

Résumé 0

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.