{
  "abstract": "This paper studies partially observed mean field games without perfect recall (WPR). The representative agent observes a noisy signal, but the control at time \\(t\\) uses only \\(\\mathcal G_t^I=σ(y_t)\\), a generally non-nested information family. The conditional population law instead uses the observation filtration \\(\\mathbb F^Y\\). These coupled levels rely on different information scales and are difficult to close within one construction. We parameterize the environment by a deterministic compatible joint law of state, driving variables, and random mean field term, thereby preserving its dependence structure without enlarging the agent's control information. For a fixed law, a reference measure and Girsanov's theorem yield a WPR stochastic maximum principle; the selected response is represented by the conditional Hamiltonian and WPR belief measure. The joint path posterior of hidden state and mean field term gives a weak Kushner-Stratonovich representation of the conditional population law. A recursive response map is continuous on a compact convex set of compatible laws, so Schauder-Tychonoff yields a weak WPR equilibrium. For a fixed equilibrium law and feedback, a compatible Yamada-Watanabe theorem lifts pathwise uniqueness to a strong realization. Finally, a linear-quadratic interbank lending example compares perfect recall (PR) with WPR. The PR response follows the Kalman-Bucy feedback, whereas the WPR response solves a Fredholm-Volterra equation and is affine in the current observation under Gaussianity. The numerical experiment illustrates how equilibrium behavior differs between PR and WPR.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.00880",
  "author_total": 3,
  "authors": [
    {
      "name": "Xuanping Zhang"
    },
    {
      "name": "Xiao Zhang"
    },
    {
      "name": "Wang Yao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3fgatwvy9nsvs.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.00880",
  "fulltext_url": null,
  "id": "3fgatwvy9nsvs",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.00880",
  "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"
    ],
    [
      "openalex",
      "2003|Stochastic processes and financial applications"
    ]
  ],
  "openalex": "W7206178496",
  "pdf_url": "https://arxiv.org/pdf/2609.00880",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3fgatwvy9nsvs.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:04Z",
      "native_id": "2609.00880",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.00880"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Partially Observed Mean Field Games Without Perfect Recall: Optimality Conditions and Equilibria",
  "title_text": "Partially Observed Mean Field Games Without Perfect Recall: Optimality Conditions and Equilibria",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:04Z",
  "url": "https://research.draconitic.com/paper/3fgatwvy9nsvs",
  "venue": "arXiv",
  "versions": []
}