{
  "id": "2001.00779",
  "version": "v1",
  "published": "2020-01-03T10:31:21.000Z",
  "updated": "2020-01-03T10:31:21.000Z",
  "title": "Efficiency Axioms for simplicial complexes",
  "authors": [
    "Ivan Martino"
  ],
  "comment": "12 pages, 1 fugure",
  "categories": [
    "math.CO",
    "math.OC"
  ],
  "abstract": "We study the notion of efficiency for cooperative games on simplicial complexes. In such games, the grand coalition $[n]$ may be forbidden, and, thus, it is a non-trivial problem to study the total number of payoff $v_{\\Delta}$ of a cooperative game $(\\Delta, v)$. We address this question in the more general setting, by characterizing the individual values that satisfy the general efficient requirement $v_{\\Delta}^{gen}$ for a generic efficiency assignment. The traditional and the probabilistic efficiency are treated as a special case of this general efficiency. Finally, we introduce a new notion of efficiency arising from the combinatorial and topological property of the simplicial complex $\\Delta$. The efficiency in this scenario is called simplicial and we characterize the individual values fulfilling this constraint.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-03T10:31:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B35",
      "05E45",
      "91A10",
      "91A35",
      "91A80"
    ],
    "keywords": [
      "simplicial complex",
      "efficiency axioms",
      "individual values",
      "cooperative game",
      "general efficient requirement"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}