Games on distributive lattices and the Shapley interaction transform

Fabien Lange, Michel Grabisch.

The paper proposes a general approach of interaction between players or attributes. It generalizes the notion of interaction defined for players modeled by games, by considering functions defined on distributive lattices. A general definition of the interaction index is provided, as well as the construction of operators establishing transforms between games, their Möbius transforms and their interaction indices.

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