{
  "id": "1904.03346",
  "version": "v1",
  "published": "2019-04-06T02:57:49.000Z",
  "updated": "2019-04-06T02:57:49.000Z",
  "title": "Linear-Quadratic Mean Field Social Optimization with a Major Player",
  "authors": [
    "Minyi Huang",
    "Son Luu Nguyen"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "This paper considers a linear-quadratic (LQ) mean field control problem involving a major player and a large number of minor players, where the dynamics and costs depend on random parameters. The objective is to optimize a social cost as a weighted sum of the individual costs under decentralized information. We apply the person-by-person optimality principle in team decision theory to the finite population model to construct two limiting variational problems whose solutions, subject to the requirement of consistent mean field approximations, yield a system of forward-backward stochastic differential equations (FBSDEs). We show the existence and uniqueness of a solution to the FBSDEs and obtain decentralized strategies nearly achieving social optimality in the original large but finite population model.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-04-06T02:57:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "linear-quadratic mean field social optimization",
      "major player",
      "finite population model",
      "consistent mean field approximations",
      "mean field control problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}