{
  "abstract": "We study contraction properties of non-stationary continuous-time mean-field games (MFGs) under discounting and entropy regularization. The state of the representative agent evolves according to a controlled continuous-time Markov chain, and both the state and action spaces are finite. In contrast to the undiscounted case, we show that, under a sufficiently large discount rate, finite-horizon MFGs admit a horizon-independent contraction condition, which also coincides with the corresponding infinite-horizon non-stationary contraction condition. As a byproduct, we obtain an explicit convergence rate between finite- and infinite-horizon mean-field equilibria. For each finite horizon, we further derive a refined contraction criterion from the spectral radius of a positive operator that majorizes the propagation of policy errors, and show that its large-horizon limit agrees with the horizon-independent contraction factor. Finally, we provide an explicit error bound between discounted and undiscounted finite-horizon regularized equilibria.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.27723",
  "author_total": 3,
  "authors": [
    {
      "name": "Junji Yan"
    },
    {
      "name": "Uğur Aydın"
    },
    {
      "name": "Tamer Başar"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/awazp2n7zvdbk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.27723",
  "fulltext_url": null,
  "id": "awazp2n7zvdbk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.27723",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.GT"
    ],
    [
      "arxiv",
      "cs.SY"
    ],
    [
      "arxiv",
      "eess.SY"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "2003|Stochastic processes and financial applications"
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  "openalex": "W7204816466",
  "pdf_url": "https://arxiv.org/pdf/2608.27723",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/awazp2n7zvdbk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:28Z",
      "native_id": "2608.27723",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.27723"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Horizon-Independent Contraction for Continuous-Time Discounted Regularized Mean-Field Games",
  "title_text": "Horizon-Independent Contraction for Continuous-Time Discounted Regularized Mean-Field Games",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:28Z",
  "url": "https://research.draconitic.com/paper/awazp2n7zvdbk",
  "venue": "arXiv",
  "versions": []
}