{
  "abstract": "In this paper, we study the closed-loop $α$-potential stochastic differential game (SDG) problem as a continuation of our prior research on open-loop control (see \\cite{GLZ2025}). By utilizing the backward stochastic differential equation (BSDE) approach, we derive a precise estimate for the parameter $α$. Compared to our earlier work \\cite{GLZ2025}, this study incorporates both first- and second-order sensitivity state processes, as well as the sensitivity of the control process. A distinguishing feature of this work is that, in the context of $N$-player heterogeneous agent games involving mean-field type interactions, we derive an $N$-uniform upper bound for the minimal potential approximation error. In contrast to the corresponding open-loop estimates, the closed-loop bound contains feedback-induced contributions that need not vanish with $N$. Consequently, our present estimate does not in general guarantee $α\\rightarrow 0$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.09756",
  "author_total": 2,
  "authors": [
    {
      "name": "Xun Li"
    },
    {
      "name": "Liangquan Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2wscjmxzhsc38.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.09756",
  "fulltext_url": null,
  "id": "2wscjmxzhsc38",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.09756",
  "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": "W7212173749",
  "pdf_url": "https://arxiv.org/pdf/2609.09756",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2wscjmxzhsc38.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:15Z",
      "native_id": "2609.09756",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.09756"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Closed-loop $α$-Potential Stochastic Differential Games via a BSDE Approach",
  "title_text": "Closed-loop α-Potential Stochastic Differential Games via a BSDE Approach",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:15Z",
  "url": "https://research.draconitic.com/paper/2wscjmxzhsc38",
  "venue": "arXiv",
  "versions": []
}