{
  "id": "2202.06835",
  "version": "v1",
  "published": "2022-02-14T16:19:29.000Z",
  "updated": "2022-02-14T16:19:29.000Z",
  "title": "Approximation of N-player stochastic games with singular controls by mean field games",
  "authors": [
    "Haoyang Cao",
    "Xin Guo",
    "Joon Seok Lee"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "This paper establishes that a class of $N$-player stochastic games with singular controls, either of bounded velocity or of finite variation, can both be approximated by mean field games (MFGs) with singular controls of bounded velocity. More specifically, it shows (i) the optimal control to an MFG with singular controls of a bounded velocity $\\theta$ is shown to be an $\\epsilon_N$-NE to an $N$-player game with singular controls of the bounded velocity, with $\\epsilon_N = O(\\frac{1}{\\sqrt{N}})$, and (ii) the optimal control to this MFG is an $(\\epsilon_N + \\epsilon_{\\theta})$-NE to an $N$-player game with singular controls of finite variation, where $\\epsilon_{\\theta}$ is an error term that depends on $\\theta$. This work generalizes the classical result on approximation $N$-player games by MFGs, by allowing for discontinuous controls.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-02-14T16:19:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "singular controls",
      "mean field games",
      "n-player stochastic games",
      "bounded velocity",
      "player game"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}