Decomposition of interaction indices: alternative interpretations of cardinal–probabilistic interaction indices
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...
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| Veröffentlicht in: | Theory and decision 2024-08, Vol.97 (1), p.139-165 |
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| creator | Courtin, Sébastien Tido Takeng, Rodrigue Chantreuil, Frédéric |
| description | 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. |
| doi_str_mv | 10.1007/s11238-023-09970-8 |
| format | Article |
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| subjects | Behavioral/Experimental Economics Cooperation Decomposition Economic Theory/Quantitative Economics/Mathematical Methods Economics Economics and Finance Finance Game Theory Humanities and Social Sciences Inequality Insurance Management Operations Research/Decision Theory Players Probability Social and Behav. Sciences Statistics for Business |
| title | Decomposition of interaction indices: alternative interpretations of cardinal–probabilistic interaction indices |
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