{
  "id": "1703.04437",
  "version": "v1",
  "published": "2017-03-13T15:12:19.000Z",
  "updated": "2017-03-13T15:12:19.000Z",
  "title": "Mean Field Games with Singular Controls of Bounded Velocity",
  "authors": [
    "Xin Guo",
    "Joon Seok Lee"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "This paper studies a class of mean field games (MFGs) with singular controls of bounded velocity. By relaxing the absolute continuity of the control process, it generalizes the MFG framework of Lasry and Lions [36] and Huang, Malham\\'e, and Caines [29]. It provides a unique solution to the MFG with explicit optimal control policies and establishes the $\\epsilon$-Nash equilibrium of the corresponding $N$-player game. Finally, it analyzes a particular MFG with explicit solutions in a systemic risk model originally formulated by Carmona, Fouque, and Sun [17] in a regular control setting.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-13T15:12:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "mean field games",
      "singular controls",
      "bounded velocity",
      "explicit optimal control policies",
      "systemic risk model"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}