{
  "id": "1801.08828",
  "version": "v1",
  "published": "2018-01-26T14:39:12.000Z",
  "updated": "2018-01-26T14:39:12.000Z",
  "title": "An ergodic problem for Mean Field Games: qualitative properties and numerical simulations",
  "authors": [
    "Simone Cacace",
    "Fabio Camilli",
    "Annalisa Cesaroni",
    "Claudio Marchi"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "This paper is devoted to some qualitative descriptions and some numerical results for ergodic Mean Field Games systems which arise, e.g., in the homogenization with a small noise limit. We shall consider either power type potentials or logarithmic type ones. In both cases, we shall establish some qualitative properties of the effective Hamiltonian $\\bar H$ and of the effective drift $\\bar b$. In particular we shall provide two cases where the effective system keeps/looses the Mean Field Games structure, namely where $\\nabla_P \\bar H(P,\\alpha)$ coincides or not with $\\bar b(P, \\alpha)$. On the other hand, we shall provide some numerical tests validating the aforementioned qualitative properties of $\\bar H$ and $\\bar b$. In particular, we provide a numerical estimate of the discrepancy $\\nabla_P \\bar H(P,\\alpha)-\\bar b(P, \\alpha)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-26T14:39:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "qualitative properties",
      "ergodic problem",
      "numerical simulations",
      "ergodic mean field games systems",
      "mean field games structure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}