Axiomatic characterizations of probabilistic and cardinal-probabilistic interaction indices

By Katsushige Fujimoto, Ivan Kojadinovic, Jean-Luc Marichal. 2006

177 citations recorded by the source corpus.

Abstract In the framework of cooperative game theory, the concept of interaction index, which can be regarded as an extension of that of value, has been recently proposed to measure the interaction phenomena among players. Axiomatizations of two classes of interaction indices, namely probabilistic interaction indices and cardinal-probabilistic interaction indices, generalizing probabilistic values and semivalues, respectively, are first proposed. The axioms we utilize are based on natural generalizations of axioms involved in the axiomatizations of values. In the second half of the paper, existing instances of cardinal-probabilistic interaction indices encountered thus far in the literature are also axiomatized.

Subfields: Artificial Intelligence, Economics and Econometrics, Management Science and Operations Research, Game & Decision Theory

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Citations in the corpus

Refining Language Models with Compositional Explanations (2021, methodology): “We borrow the definition of interaction from the cooperative game theory [10].”
Consistent Individualized Feature Attribution for Tree Ensembles (2018, methodology): “To directly capture pairwise interaction effects we propose SHAP interaction values; an extension of SHAP values based on the Shapley interaction index from game theory [12].”
A review of methods for capacity identification in Choquet integral based multi-attribute utility theory: Applications of the Kappalab R package (2008, background): “More generally, it can be shown that a k -additive capacity, k ∈ { 2 , . . . , n } , can model interaction among at most k criteria; see e.g. [ 26].”
A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid (2008, background): “This section is based on Grabisch and Labreuche (2001). The main concern here is to know on which criteria acts should be improved on average so as to reach the highest possible global score.”
Explainable AI for Trees: From Local Explanations to Global Understanding (2019, methodology): “If we use the same definition of fx that we used to get Sabaas values and SHAP values, but with the Shapley interaction index, we get SHAP interaction values [21], defined as:”