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: Normandie University, UNICAEN, IDEES UMR 6266
Rodrigue Tido Takeng: Université de Caen Normandie, CREM, UMR 6211
Frédéric Chantreuil: University of La Reunion, CEMOI

Theory and Decision, 2024, vol. 97, issue 1, No 7, 139-165

Abstract: Abstract In cooperative game theory, the concept of interaction index is an extension of the concept of one-point solution that takes into account interactions among players. In this paper, we focus on cardinal–probabilistic interaction indices that generalize 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 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 characterizations of the cardinal–probabilistic interaction indices.

Keywords: Game theory; Cardinal–probabilistic interaction indices; External interaction index; Decomposition (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s11238-023-09970-8

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