{
  "id": "0902.2770",
  "version": "v1",
  "published": "2009-02-16T20:17:30.000Z",
  "updated": "2009-02-16T20:17:30.000Z",
  "title": "Equilibrium payoffs in finite games",
  "authors": [
    "Ehud Lehrer",
    "Eilon Solan",
    "Yannick Viossat"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "We study the structure of the set of equilibrium payoffs in finite games, both for Nash equilibrium and correlated equilibrium. A nonempty subset of R^2 is shown to be the set of Nash equilibrium payoffs of a bimatrix game if and only if it is a finite union of rectangles. Furthermore, we show that for any nonempty finite union of rectangles U and any polytope P in R^2 containing U, there exists a bimatrix game with U as set of Nash equilibrium payoffs and P as set of correlated equilibrium payoffs. The n-player case and the robustness of this result to perturbation of the payoff matrices are also studied.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-02-16T20:17:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "91A10"
    ],
    "keywords": [
      "finite games",
      "nash equilibrium payoffs",
      "bimatrix game",
      "nonempty finite union",
      "nonempty subset"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0902.2770L"
    }
  }
}