Cooperative games on simplicial complexes

Abstract: In this work, we define cooperative games on simplicial complexes, generalizing the study of probabilistic values of Weber and quasi-probabilistic values of Bilbao, Driessen, Jim\'{e}nez Losada and Lebr\'{o}n. Applications to Multi-Touch Attribution and the interpretability of the Machine-Learning prediction models motivate these new developments. We deal with the axiomatization provided by the $\lambda_i$-dummy and the monotonicity requirements together with a probabilistic form of the symmetric and the efficiency axioms. We also characterize combinatorially the set of probabilistic participation influences as the facet polytope of the simplicial complex.