Cooperative games on simplicial complexes
Ivan Martino · Discrete Applied Mathematics · 2020
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 λi-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.