{
  "id": "2202.08163",
  "version": "v1",
  "published": "2022-02-16T16:12:20.000Z",
  "updated": "2022-02-16T16:12:20.000Z",
  "title": "Propagation of Chaos of Forward-Backward Stochastic Differential Equations with Graphon Interactions",
  "authors": [
    "Erhan Bayraktar",
    "Ruoyu Wu",
    "Xin Zhang"
  ],
  "comment": "Keywords: Large population games, graphon mean field games, propagation of chaos, FBSDE, convergence of Nash equilibrium",
  "categories": [
    "math.PR",
    "math.OC"
  ],
  "abstract": "In this paper, we study graphon mean field games using a system of forward-backward stochastic differential equations. We establish the existence and uniqueness of solutions under two different assumptions and prove the stability with respect to the interacting graphons which are necessary to show propagation of chaos results. As an application of propagation of chaos, we prove the convergence of n-player game Nash equilibrium for a general model, which is new in the theory of graphon mean field games.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-02-16T16:12:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "49N80",
      "60F25",
      "91A06",
      "91A15"
    ],
    "keywords": [
      "forward-backward stochastic differential equations",
      "graphon interactions",
      "propagation",
      "study graphon mean field games",
      "n-player game nash equilibrium"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}