{
  "abstract": "We introduce an admissible trembling-hand refinement for stochastic mean field games formulated through relaxed controlled martingale problems. A relaxed MFG equilibrium is perfect if it is the common Wasserstein limit of two sequences of joint control-state laws. The first consists of full-support population perturbations admissible for the state laws they generate; the second consists of exact optimal responses to those perturbed state laws. This admissibility condition prevents the control and state coordinates of a perturbation from being varied independently. Under the standing continuity, growth, and coercivity assumptions, we prove existence without requiring compact controls or bounded coefficients. The proof combines a perturbed fixed-point argument in the compact-bounded case with truncation, uniform moment estimates, compactness, and stability of controlled martingale problems. A one-dimensional model with exactly two relaxed mean field game equilibria shows that the refinement is genuinely selective: only one equilibrium is trembling-hand perfect.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.05083",
  "author_total": 3,
  "authors": [
    {
      "name": "Luciano Campi"
    },
    {
      "name": "Luca Di Persio"
    },
    {
      "name": "Lucrezia Zorzi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dqpm9353mhvj6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.05083",
  "fulltext_url": null,
  "id": "dqpm9353mhvj6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.05083",
  "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": "W7211869449",
  "pdf_url": "https://arxiv.org/pdf/2609.05083",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dqpm9353mhvj6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:18Z",
      "native_id": "2609.05083",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.05083"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Trembling-Hand Perfection in Mean Field Games",
  "title_text": "Trembling-Hand Perfection in Mean Field Games",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:18Z",
  "url": "https://research.draconitic.com/paper/dqpm9353mhvj6",
  "venue": "arXiv",
  "versions": []
}