{
  "id": "2001.00366",
  "version": "v1",
  "published": "2020-01-02T09:25:06.000Z",
  "updated": "2020-01-02T09:25:06.000Z",
  "title": "Cooperative games on simplicial complexes",
  "authors": [
    "Ivan Martino"
  ],
  "comment": "16 pages, 2 figures",
  "categories": [
    "math.CO",
    "math.OC"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-02T09:25:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "91A12",
      "91A46",
      "05E45",
      "05E99",
      "52B05",
      "52B40"
    ],
    "keywords": [
      "simplicial complex",
      "probabilistic participation influences",
      "machine-learning prediction models motivate",
      "facet polytope",
      "quasi-probabilistic values"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}