{
  "abstract": "The recently introduced framework of $α$-potential games facilitates the analysis of finite-player dynamic games by reducing the search for approximate Nash equilibria to the minimization of a single $α$-potential function. In this work, we show that the approximate potential structure of finite-player games persists in the large-population limit, leading naturally to a notion of $α$-potential mean field games (MFGs). Specifically, we show that both the optimal values and the minimizers of normalized $N$-player $α_N$-potential functions converge to those of a mean field control (MFC) problem with measure-valued controls. We identify the objective of this limiting MFC problem as an $α_\\infty$-potential function for an MFG, and characterize the parameter $α_\\infty$ analytically. We further show that $\\lim_{N\\to\\infty}α_N= 0$ is equivalent to standard conditions for potential MFGs, in which case the limiting MFC objective becomes a potential function for the MFG. Together, these results provide new constructions of potential MFGs from finite-player games through the asymptotic condition $\\lim_{N\\to \\infty}α_N= 0$, and establish propagation of chaos of potential-selected equilibria from $N$-player games to MFGs with general controlled diffusions, common noise, and non-separable state-control interactions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.09815",
  "author_total": 3,
  "authors": [
    {
      "name": "Xin Guo"
    },
    {
      "name": "Meng Wang"
    },
    {
      "name": "Yufei Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4az2nm30acywh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.09815",
  "fulltext_url": null,
  "id": "4az2nm30acywh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.09815",
  "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",
      "math.OC"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2003|Stochastic processes and financial applications"
    ]
  ],
  "openalex": "W7163991322",
  "pdf_url": "https://arxiv.org/pdf/2606.09815",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4az2nm30acywh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2606.09815",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.09815"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Limit Theory for $N$-Player $α$-Potential Games",
  "title_text": "Limit Theory for N-Player α-Potential Games",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/4az2nm30acywh",
  "venue": "arXiv",
  "versions": []
}