{
  "id": "1602.06140",
  "version": "v1",
  "published": "2016-02-19T13:16:16.000Z",
  "updated": "2016-02-19T13:16:16.000Z",
  "title": "A probabilistic representation for the value of zero-sum differential games with incomplete information on both sides",
  "authors": [
    "Fabien Gensbittel",
    "Catherine Rainer"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "We prove that for a class of zero-sum differential games with incomplete information on both sides, the value admits a probabilistic representation as the value of a zero-sum stochastic differential game with complete information, where both players control a continuous martingale. A similar representation as a control problem over discontinuous martingales was known for games with incomplete information on one side (see Cardaliaguet-Rainer [8]), and our result is a continuous-time analog of the so called splitting-game introduced in Laraki [20] and Sorin [27] in order to analyze discrete-time models. It was proved by Cardaliaguet [4, 5] that the value of the games we consider is the unique solution of some Hamilton-Jacobi equation with convexity constraints. Our result provides therefore a new probabilistic representation for solutions of Hamilton-Jacobi equations with convexity constraints as values of stochastic differential games with unbounded control spaces and unbounded volatility.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-02-19T13:16:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "zero-sum differential games",
      "incomplete information",
      "probabilistic representation",
      "zero-sum stochastic differential game",
      "hamilton-jacobi equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}