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Interaction indices for multichoice games

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Abstract

Models in Multicriteria Decision Analysis (MCDA) can be analyzed by means of an importance index and an interaction index for every group of criteria. We consider first discrete models in MCDA, without further restriction, which amounts to considering multichoices games, that is, cooperative games with several levels of participation. We propose and axiomatize two interaction indices for multichoice games: the signed interaction index and the absolute interaction index. In a second part, we consider the continuous case, supposing that the continuous model is obtained from a discrete one by means of the Choquet integral. We show that, as in the case of classical games, the interaction index defined for continuous aggregation functions coincides with the (signed) interaction index, up to a normalizing coefficient

Suggested Citation

  • Mustapha Ridaoui & Michel Grabisch & Christophe Labreuche, 2019. "Interaction indices for multichoice games," Documents de travail du Centre d'Economie de la Sorbonne 19019, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    • Handle: RePEc:mse:cesdoc:19019
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    Cited by:

    1. Michel Grabisch & Christophe Labreuche, 2016. "Fuzzy Measures and Integrals in MCDA," International Series in Operations Research & Management Science, in: Salvatore Greco & Matthias Ehrgott & José Rui Figueira (ed.), Multiple Criteria Decision Analysis, edition 2, chapter 0, pages 553-603, Springer.
    2. Lowing, David & Techer, Kevin, 2025. "Toward a consensus on extended Shapley values for multi-choice games," Mathematical Social Sciences, Elsevier, vol. 137(C).
    3. Christophe Labreuche & Michel Grabisch, 2006. "Axiomatization of the Shapley value and power index for bi-cooperative games," Cahiers de la Maison des Sciences Economiques b06023, Université Panthéon-Sorbonne (Paris 1).

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    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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