{
  "abstract": "We study entropy-regularized exploratory control in finite $N$-player stochastic differential games under a response model in which each player conditions on the opponents' currently realized actions and evaluates continuation with that profile frozen. The resulting Gibbs best responses form a system of full conditional densities, which need not admit a common joint law. We characterize joint realizability by a cross-partial condition on the entropy-scaled Hamiltonian gradients and, on simply connected action domains, by an equivalent entropy-weighted potential structure. When compatibility fails, a coordinate-path construction yields a joint density whose full conditionals satisfy explicit quadratic Kullback--Leibler bounds. We extend the analysis to stationary discounted problems and derive martingale and policy-improvement characterizations for learning the frozen response maps. A two-player linear-quadratic example illustrates the compatibility criterion and the associated learning procedure.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.19928",
  "author_total": 1,
  "authors": [
    {
      "name": "Jisheng Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7xvpk7fd86hmr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.19928",
  "fulltext_url": null,
  "id": "7xvpk7fd86hmr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.19928",
  "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",
      "1803|Game Theory and Applications"
    ]
  ],
  "openalex": "W7170185909",
  "pdf_url": "https://arxiv.org/pdf/2607.19928",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7xvpk7fd86hmr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2607.19928",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.19928"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Continuous-Time Reinforcement Learning for $N$-Player Stochastic Differential Games with Exploratory Policies",
  "title_text": "Continuous-Time Reinforcement Learning for N-Player Stochastic Differential Games with Exploratory Policies",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/7xvpk7fd86hmr",
  "venue": "arXiv",
  "versions": []
}