{
  "id": "1807.04795",
  "version": "v1",
  "published": "2018-07-12T19:25:15.000Z",
  "updated": "2018-07-12T19:25:15.000Z",
  "title": "Mean Field Game with Delay: a Toy Model",
  "authors": [
    "Jean-Pierre Fouque",
    "Zhaoyu Zhang"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We study a toy model of linear-quadratic mean field game with delay. We \"lift\" the delayed dynamic into an infinite dimensional space, and recast the mean field game system which is made of a forward Kolmogorov equation and a backward Hamilton-Jacobi-Bellman equation. We identify the corresponding master equation. A solution to this master equation is computed, and we show that it provides an approximation to a Nash equilibrium of the finite player game.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-07-12T19:25:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "91A15",
      "91G80",
      "60G99"
    ],
    "keywords": [
      "toy model",
      "linear-quadratic mean field game",
      "mean field game system",
      "finite player game",
      "infinite dimensional space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}