{
  "abstract": "We develop and analyze a projected extragradient method, preconditioned by a Riesz map, for a first-order price-formation mean field game in one space dimension. The model couples Hamilton--Jacobi--Bellman and transport equations through a global market-clearing constraint. Finite propagation justifies truncating the first-order transport equation to a bounded interval. A monotone weak formulation incorporates the mixed initial--terminal data. Its Riesz map uses $L^2$ norms for density and price directions and a space-time $H^1$ norm for value-function directions, preconditioning the residual without adding higher-order regularization terms to the MFG equations. A density-only argument rules out cocoercivity on the localized admissible set in every equivalent Hilbert metric, motivating extragradient updates. For $H(x,p)=p^2/2$, we use a monotone upwind discretization with adjoint-consistent transport and a state-constraint boundary closure. We establish a mesh-independent Lipschitz bound on bounded convex admissible sets with uniform density, slope, and price bounds. With exact metric projection onto these sets, the iteration converges to a solution of the discrete variational inequality on each fixed grid, with an admissible step-size threshold independent of both mesh sizes. Convergence under mesh refinement is not proved. On a quadratic benchmark, all reported runs reach the stopping tolerance with one fixed step size across a factor-of-16 reduction in both mesh sizes. Price errors and value-function errors measured away from low-density regions decay approximately at first order under refinement, while density errors decrease more slowly.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.13934",
  "author_total": 2,
  "authors": [
    {
      "name": "Yeva Gevorgyan"
    },
    {
      "name": "Diogo Gomes"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1pa1f8mczrapy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.13934",
  "fulltext_url": null,
  "id": "1pa1f8mczrapy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.13934",
  "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.AP"
    ],
    [
      "openalex",
      "2003|Stochastic processes and financial applications"
    ]
  ],
  "openalex": "W7221544208",
  "pdf_url": "https://arxiv.org/pdf/2610.13934",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1pa1f8mczrapy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2610.13934",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.13934"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A Riesz-Map Preconditioned Extragradient Method for Price Formation in Mean Field Games",
  "title_text": "A Riesz-Map Preconditioned Extragradient Method for Price Formation in Mean Field Games",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/1pa1f8mczrapy",
  "venue": "arXiv",
  "versions": []
}