{
  "id": "1508.03921",
  "version": "v1",
  "published": "2015-08-17T04:02:02.000Z",
  "updated": "2015-08-17T04:02:02.000Z",
  "title": "Non-zero-sum stopping games in continuous time",
  "authors": [
    "Zhou Zhou"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "On a filtered probability space $(\\Omega ,\\mathcal{F}, (\\mathcal{F}_t)_{t\\in[0,\\infty]}, \\mathbb{P})$, we consider the two-player non-zero-sum stopping game $u^i := \\mathbb{E}[U^i(\\rho,\\tau)],\\ i=1,2$, where the first player choose a stopping strategy $\\rho$ to maximize $u^1$ and the second player chose a stopping strategy $\\tau$ to maximize $u^2$. Unlike the Dynkin game, here we assume that $U(s,t)$ is $\\mathcal{F}_{s\\vee t}$-measurable. Assuming the continuity of $U^i$ in $(s,t)$, we show that there exists an $\\epsilon$-Nash equilibrium for any $\\epsilon>0$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-08-17T04:02:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "continuous time",
      "two-player non-zero-sum stopping game",
      "second player chose",
      "first player choose",
      "stopping strategy"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150803921Z"
    }
  }
}