{
  "id": "2107.03273",
  "version": "v1",
  "published": "2021-07-07T15:07:13.000Z",
  "updated": "2021-07-07T15:07:13.000Z",
  "title": "Closed-loop convergence for mean field games with common noise",
  "authors": [
    "Daniel Lacker",
    "Luc Le Flem"
  ],
  "comment": "47 pages",
  "categories": [
    "math.PR",
    "math.OC"
  ],
  "abstract": "This paper studies the convergence problem for mean field games with common noise. We define a suitable notion of weak mean field equilibria, which we prove captures all subsequential limit points, as $n\\to\\infty$, of closed-loop approximate equilibria from the corresponding $n$-player games. This extends to the common noise setting a recent result of the first author, while also simplifying a key step in the proof and allowing unbounded coefficients and non-i.i.d. initial conditions. Conversely, we show that every weak mean field equilibrium arises as the limit of some sequence of approximate equilibria for the $n$-player games, as long as the latter are formulated over a broader class of closed-loop strategies which may depend on an additional common signal.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-07-07T15:07:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "mean field games",
      "common noise",
      "closed-loop convergence",
      "weak mean field equilibrium arises",
      "player games"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 47,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}