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, Jimenez Losada and Lebron. 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.

中文翻译：

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单纯复形上的合作博弈

在这项工作中，我们定义了单纯复形上的合作博弈，概括了 Weber 的概率值和 Bilbao、Driessen、Jimenez Losada 和 Lebron 的准概率值的研究。多点触控归因的应用和机器学习预测模型的可解释性推动了这些新的发展。我们处理 $\lambda_i$-dummy 提供的公理化和单调性要求以及对称和效率公理的概率形式。我们还将概率参与影响集的组合特征描述为单纯复形的多面体。