{
  "abstract": "This paper analyzes graphexon mean field games (GXMFG) on large network limits. By considering edge distributions of a sequence of finite graphs, we define the empirical graphexon measures and study their subsequential weak limits in a graphexon space consisting of all symmetric probability measures on $[0,1]^{2d}$. This concept of network limits extends graphon theory to general, not necessarily dense, networks. To formulate the game using the graphexon limit, we exploit a useful property that a probability measure on a product space is the product of a probability kernel and a marginal distribution. Based on such graph limits and the probability kernel of the associated graphexon measure, we derive the GXMFG equations, and present a detailed analysis for the linear-quadratic case. For linear-quadratic models with finite populations residing over large networks, we use the GXMFG equations to construct decentralized strategies, for which an $ε$-Nash equilibrium property is established.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.27292",
  "author_total": 2,
  "authors": [
    {
      "name": "Peter E. Caines"
    },
    {
      "name": "Minyi Huang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2av6gyxxza9kx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.27292",
  "fulltext_url": null,
  "id": "2av6gyxxza9kx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.27292",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "2003|Stochastic processes and financial applications"
    ]
  ],
  "openalex": "W7223105214",
  "pdf_url": "https://arxiv.org/pdf/2610.27292",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2av6gyxxza9kx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2610.27292",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.27292"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Graphexon Mean Field Games on Large Network Limits",
  "title_text": "Graphexon Mean Field Games on Large Network Limits",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/2av6gyxxza9kx",
  "venue": "arXiv",
  "versions": []
}