Cooperative games on simplicial complexes

In this work, we define cooperative games on simplicial complexes, generalizing the study of probabilistic values of Weber (1988) and quasi-probabilistic values of Bilbao et al. (2001). Applications to Multi-Touch Attribution and the interpretability of the Machine-Learning prediction models motivate these new developments (Lundberg and Lee, 2017; Ribeiro et al., 2016; Strumbelj and Kononenko, 2013; Shrikumar et al., 2017; Datta et al., 2016; Bach et al., 2015). 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. (C) 2020 The Author(s). Published by Elsevier B.V.