An axiomatic approach to the concept of interaction among players in cooperative games

An axiomatization of the interaction between the players of any coalition is given. It is based on three axioms: linearity, dummy land symmetry. These interaction indices extend the Banzhaf and Shapley values when using in addition two equivalent recursive axioms. Lastly, we give an expression of the Banzhaf and Shapley interaction indices in terms of pseudo-Boolean functions.