{
  "id": "2106.09405",
  "version": "v1",
  "published": "2021-06-17T11:42:58.000Z",
  "updated": "2021-06-17T11:42:58.000Z",
  "title": "Mertens conjectures in absorbing games with incomplete information",
  "authors": [
    "Bruno Ziliotto"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "In a zero-sum stochastic game with signals, at each stage, two adversary players take decisions and receive a stage payoff determined by these decisions and a variable called state. The state follows a Markov chain, that is controlled by both players. Actions and states are imperfectly observed by players, who receive a private signal at each stage. Mertens (ICM 1986) conjectured two properties regarding games with long duration: first, that limit value always exists, second, that when Player 1 is more informed than Player 2, she can guarantee uniformly the limit value. These conjectures were disproved recently by the author, but remain widely open in many subclasses. A well-known particular subclass is the one of absorbing games with incomplete information on both sides, in which the state can move at most once during the game, and players get a private signal about it at the outset of the game. This paper proves Mertens conjectures in this particular model, by introducing a new approximation technique of belief dynamics, that is likely to generalize to many other frameworks. In particular, this makes a significant step towards the understanding of the following broad question: in which games do Mertens conjectures hold?",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-17T11:42:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "91A15",
      "60G42"
    ],
    "keywords": [
      "incomplete information",
      "absorbing games",
      "private signal",
      "limit value",
      "zero-sum stochastic game"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}