{
  "id": "1506.04594",
  "version": "v1",
  "published": "2015-06-15T13:51:26.000Z",
  "updated": "2015-06-15T13:51:26.000Z",
  "title": "On the mean field games with common noise and the McKean-Vlasov SPDEs",
  "authors": [
    "Vassili Kolokoltsov",
    "Marianna Troeva"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We formulate the MFG limit for $N$ interacting agents with a common noise as a single quasi-linear deterministic infinite-dimensional partial differential second order backward equation. We prove that any its (regular enough) solution provides an $1/N$-Nash-equilibrium profile for the initial $N$-player game. We use the method of stochastic characteristics to provide the link with the basic models of MFG with a major player. We develop two auxiliary theories of independent interest: sensitivity and regularity analysis for the McKean-Vlasov SPDEs and the $1/N$-convergence rate for the propagation of chaos property of interacting diffusions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-06-15T13:51:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "mean field games",
      "common noise",
      "mckean-vlasov spdes",
      "partial differential second order",
      "infinite-dimensional partial differential second"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150604594K"
    }
  }
}