{
  "id": "1904.13287",
  "version": "v1",
  "published": "2019-04-30T14:51:32.000Z",
  "updated": "2019-04-30T14:51:32.000Z",
  "title": "Weak KAM theory for potential MFG",
  "authors": [
    "Pierre Cardaliaguet",
    "Marco Masoero"
  ],
  "categories": [
    "math.AP",
    "math.DS"
  ],
  "abstract": "We develop the counterpart of weak KAM theory for potential mean field games. This allows to describe the long time behavior of time-dependent potential mean field game systems. Our main result is the existence of a limit, as time tends to infinity, of the value function of an optimal control problem stated in the space of measures. In addition, we show a mean field limit for the ergodic constant associated with the corresponding Hamilton-Jacobi equation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-04-30T14:51:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "49J20",
      "37K55",
      "37A99"
    ],
    "keywords": [
      "weak kam theory",
      "potential mfg",
      "potential mean field game systems",
      "time-dependent potential mean field game",
      "long time behavior"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}