{
  "id": "1912.12873",
  "version": "v1",
  "published": "2019-12-30T10:39:13.000Z",
  "updated": "2019-12-30T10:39:13.000Z",
  "title": "Does randomization matter in dynamic games?",
  "authors": [
    "Enxian Chen",
    "Wei He",
    "Yeneng Sun",
    "Hanping Xu"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "This paper investigates mixed strategies in dynamic games with perfect information. We present an example to show that a player may obtain higher payoff by playing mixed strategy. By contrast, the main result of the paper shows that every two-player dynamic zero-sum game with nature has the no-mixing property, which implies that mixed strategy is useless in this most classical class of games. As for applications, we show the existence of pure-strategy subgame-perfect equilibria in two-player zero-sum games with nature. Based on the main result, we also prove the existence of a universal subgame-perfect equilibrium that can induce all the pure-strategy subgame-perfect equilibria in such games. A generalization of the main result for multiple players and some further results are also discussed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-30T10:39:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dynamic games",
      "randomization matter",
      "pure-strategy subgame-perfect equilibria",
      "main result",
      "mixed strategy"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}