{
  "abstract": "We study a class of linear-quadratic mean field games in which the state of each agent follows a stochastic Volterra equation of convolution type. The resulting dynamics are non-Markovian and account for memory effects through a completely monotone kernel, while the mean field interaction enters both the drift and diffusion coefficients. Exploiting a Markovian lifting of the Volterra dynamics, which restores the Markov property at the price of moving to an infinite-dimensional state space, we characterize the optimal response of a representative agent for a given population mean through a system of Riccati equations in Banach spaces, thereby obtaining a feedback representation of the optimal control. We then study the consistency condition defining the mean field equilibrium, which reduces to a forward-backward fixed point equation for the equilibrium mean: we prove existence and uniqueness of the equilibrium on short horizons and, when the control does not act on the diffusion coefficient, on arbitrary horizons under a monotonicity condition on the interaction. Finally, we consider the corresponding finite-player game and establish a quantitative propagation of chaos result. As a consequence, the feedback control of any mean field equilibrium, when implemented by each agent on its own state, yields an $\\varepsilon_N$-Nash equilibrium for the $N$-player game, with an explicit rate as the number of agents tends to infinity.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.37622",
  "author_total": 3,
  "authors": [
    {
      "name": "Niccolò Fontana"
    },
    {
      "name": "Mattia Martini"
    },
    {
      "name": "Huyên Pham"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2hb2bbdprnpdq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.37622",
  "fulltext_url": null,
  "id": "2hb2bbdprnpdq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.37622",
  "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": "W7224131416",
  "pdf_url": "https://arxiv.org/pdf/2610.37622",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2hb2bbdprnpdq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.37622",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.37622"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Linear-quadratic mean field games with Volterra dynamics",
  "title_text": "Linear-quadratic mean field games with Volterra dynamics",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/2hb2bbdprnpdq",
  "venue": "arXiv",
  "versions": []
}