{
  "id": "1711.01063",
  "version": "v1",
  "published": "2017-11-03T08:54:19.000Z",
  "updated": "2017-11-03T08:54:19.000Z",
  "title": "Existence and uniqueness for Mean Field Games with state constraints",
  "authors": [
    "Piermarco Cannarsa",
    "Rossana Capuani"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "In this paper, we study deterministic mean field games for agents who operate in a bounded domain. In this case, the existence and uniqueness of Nash equilibria cannot be deduced as for unrestricted state space because, for a large set of initial conditions, the uniqueness of the solution to the associated minimization problem is no longer guaranteed. We attack the problem by interpreting equilibria as measures in a space of arcs. In such a relaxed environment the existence of solutions follows by set-valued fixed point arguments. Then, we give a uniqueness result for such equilibria under a classical monotonicity assumption.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-11-03T08:54:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "49J15",
      "49J30",
      "49J53",
      "49N90"
    ],
    "keywords": [
      "state constraints",
      "uniqueness",
      "study deterministic mean field games",
      "equilibria",
      "monotonicity assumption"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}