Cooperative games on simplicial complexes

TL;DR

This paper introduces cooperative games on simplicial complexes, extending existing frameworks to improve interpretability in machine learning and multi-touch attribution through new axiomatic characterizations.

Contribution

It generalizes cooperative game theory to simplicial complexes, providing axiomatic foundations and combinatorial characterizations for probabilistic values.

Findings

Characterizes probabilistic participation influences as facet polytopes

Provides axiomatization using dummy and monotonicity axioms

Applications to machine learning interpretability and attribution

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.