{
  "abstract": "We study atomic splittable congestion games with $n\\ge2$ players and nondecreasing $C^2$ resource costs $f$ with convex $x\\mapsto xf(x)$. We characterize the largest resource cost class for which the Nash equilibrium is unique. This characterization combines a curvature inequality involving the first two derivatives and the number of players with strict increase of the scalar marginal costs $x\\mapsto f(x)+xf'(x)$. The proof rests on first characterizing the largest resource cost classes for which the associated variational inequality operator is monotone, strictly monotone, or strongly monotone. We also draw a perhaps surprising connection to learning dynamics: the same curvature inequality characterizes universal local and global stability of Euclidean-regularized Frank--Wolfe dynamics on arbitrary compact convex strategy spaces. Both the uniqueness and stability characterizations assume closure under positive affine transformations. Both characterizations remain exact for network games; the necessity constructions use acyclic directed graphs whose arc costs can be chosen strictly positive. Finally, we show that on parallel-link networks, every interior equilibrium of the regularized Frank--Wolfe dynamics is locally exponentially stable even without the curvature condition.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.17684",
  "author_total": 1,
  "authors": [
    {
      "name": "Tobias Harks"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dzgesjp0jh7d6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.17684",
  "fulltext_url": null,
  "id": "dzgesjp0jh7d6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.17684",
  "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",
      "cs.GT"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "1803|Game Theory and Applications"
    ]
  ],
  "openalex": "W7169836535",
  "pdf_url": "https://arxiv.org/pdf/2607.17684",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dzgesjp0jh7d6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2607.17684",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.17684"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Monotonicity, Uniqueness and Frank--Wolfe Dynamics in Atomic Splittable Congestion Games",
  "title_text": "Monotonicity, Uniqueness and Frank--Wolfe Dynamics in Atomic Splittable Congestion Games",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/dzgesjp0jh7d6",
  "venue": "arXiv",
  "versions": []
}