{
  "abstract": "Many stochastic systems in operations and economics exhibit feedback between their long-run state distribution and the transition law governing their dynamics. In this paper, we develop a computational framework for stationary equilibria in such measure-dependent Markov systems when this feedback operates through a finite-dimensional aggregate. We show that the original stationary-equilibrium problem can be reduced to a finite-dimensional self-consistency equation, separating steady-state analysis of the underlying Markov system from equilibrium computation. We use properties of the resulting self-consistency map to guide the choice among fixed-point iteration, relaxed fixed-point iteration, and minimization of the fixed-point residual. The last approach requires derivatives of the self-consistency map, which are typically unavailable in closed form. We therefore develop finite-time infinitesimal perturbation analysis estimators for these derivatives, with error bounds that separate Monte Carlo error from finite-time bias. We illustrate the framework through a strategic $G/G/c$ queue and an opinion-dynamics model, showing how different structural properties lead naturally to different equilibrium-computation methods.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.17584",
  "author_total": 3,
  "authors": [
    {
      "name": "Jing Dong"
    },
    {
      "name": "Bar Light"
    },
    {
      "name": "Xin Tong"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ex7bgcz94cqdn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.17584",
  "fulltext_url": null,
  "id": "ex7bgcz94cqdn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.17584",
  "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",
      "cs.GT"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "1404|Advanced Queuing Theory Analysis"
    ]
  ],
  "openalex": "W7213517055",
  "pdf_url": "https://arxiv.org/pdf/2609.17584",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ex7bgcz94cqdn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:04Z",
      "native_id": "2609.17584",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.17584"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Computing Stationary Equilibria in Measure-Dependent Markov Systems",
  "title_text": "Computing Stationary Equilibria in Measure-Dependent Markov Systems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:04Z",
  "url": "https://research.draconitic.com/paper/ex7bgcz94cqdn",
  "venue": "arXiv",
  "versions": []
}