{
  "id": "2407.18539",
  "version": "v1",
  "published": "2024-07-26T06:38:09.000Z",
  "updated": "2024-07-26T06:38:09.000Z",
  "title": "Variational Analysis of Generalized Games over Banach spaces",
  "authors": [
    "Asrifa Sultana",
    "Shivani Valecha"
  ],
  "categories": [
    "math.OC",
    "math.FA"
  ],
  "abstract": "We study generalized games defined over Banach spaces using variational analysis. To reformulate generalized games as quasi-variational inequality problems, we will first form a suitable principal operator and study some significant properties of this operator. Then, we deduce the sufficient conditions under which an equilibrium for the generalized game can be obtained by solving a quasi-variational inequality. Based on this variational reformulation, we derive the existence of equilibrium for generalized games with non-ordered (that is, associated weak preference relations need not be complete and transitive) and mid-point continuous preference maps.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-26T06:38:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "49J40",
      "49J53",
      "91B06",
      "91B42"
    ],
    "keywords": [
      "variational analysis",
      "banach spaces",
      "quasi-variational inequality problems",
      "associated weak preference relations",
      "mid-point continuous preference maps"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}