This paper introduces four alternative representations of a set function: the Mobius transformation, the co-Mobius transformation, and the interactions between elements of any subset of a given set as extensions of Shapley and Banzhaf values. The links between the five equivalent representations...

An axiomatization of the interactions between the palyers of any coalition is given. It is based on three axioms: linearity, dummy and symmetry. These interaction indices extend the Banzhaf and Shapley values when using in addition two equivalent recursive axioms. Lastly, the authors give an...

The subsignatures of a system with continuous and exchangeable component lifetimes form a class of indexes ranging from the Samaniego signature to the Barlow–Proschan importance index. These indexes can be computed through explicit linear expressions involving the values of the structure...