{
  "id": "2312.07770",
  "version": "v1",
  "published": "2023-12-12T22:27:40.000Z",
  "updated": "2023-12-12T22:27:40.000Z",
  "title": "On Time-Inconsistency in Mean Field Games",
  "authors": [
    "Erhan Bayraktar",
    "Zhenhua Wang"
  ],
  "categories": [
    "math.OC",
    "cs.GT",
    "math.PR"
  ],
  "abstract": "We investigate an infinite-horizon time-inconsistent mean-field game (MFG) in a discrete time setting. We first present a classic equilibrium for the MFG and its associated existence result. This classic equilibrium aligns with the conventional equilibrium concept studied in MFG literature when the context is time-consistent. Then we demonstrate that while this equilibrium produces an approximate optimal strategy when applied to the related $N$-agent games, it does so solely in a precommitment sense. Therefore, it cannot function as a genuinely approximate equilibrium strategy from the perspective of a sophisticated agent within the $N$-agent game. To address this limitation, we propose a new consistent equilibrium concept in both the MFG and the $N$-agent game. We show that a consistent equilibrium in the MFG can indeed function as an approximate consistent equilibrium in the $N$-agent game. Additionally, we analyze the convergence of consistent equilibria for $N$-agent games toward a consistent MFG equilibrium as $N$ tends to infinity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-12-12T22:27:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "mean field games",
      "agent game",
      "infinite-horizon time-inconsistent mean-field game",
      "time-inconsistency",
      "classic equilibrium aligns"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}