{
  "id": "1905.08112",
  "version": "v1",
  "published": "2019-05-20T13:45:15.000Z",
  "updated": "2019-05-20T13:45:15.000Z",
  "title": "A Note On Orthogonal Decomposition of Finite Games",
  "authors": [
    "Changxi Li",
    "Daizhan Cheng",
    "Fenghua He"
  ],
  "comment": "4 pages, 2019 IEEE CDC conference paper (submitted)",
  "categories": [
    "math.OC"
  ],
  "abstract": "Various decomposition of finite games have been proposed. The inner product of vectors plays a key role in the decomposition of finite games. This paper considers the effect of different inner products on the orthogonal decomposition of finite games. We find that only when the compatible condition is satisfied, a common decomposition can be induced by the standard inner product and the weighted inner product. To explain the result, we studied the existing decompositions, including potential based decomposition, zero-sum based decomposition, and symmetry based decomposition.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-20T13:45:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite games",
      "orthogonal decomposition",
      "standard inner product",
      "vectors plays",
      "common decomposition"
    ],
    "tags": [
      "conference paper"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}