{
  "abstract": "Developing general-purpose algorithms with global asymptotic convergence guarantees for Nash equilibria of general-sum games remains a longstanding challenge. This paper extends the fixed-point bundle framework for finite-dimensional variational inequalities (VIs) from simplex domains to product-of-simplex domains, enabling its direct application to Nash equilibrium computation. The resulting fixed-point bundle exhibits a composite fiber bundle structure. The key innovation is to construct an equivalent VI on a simplex and establish the equivalence between the two fixed-point bundle frameworks via a fiber bundle isomorphism. Exploiting this geometric equivalence, we show that the path-following algorithm for VIs on product-of-simplex domains inherits the global linear convergence guarantees of the simplex-domain framework. In numerical experiments, the algorithm attained a precision of $10^{-5}$ on all 5600 randomly generated game instances, with dimension ranging from 2-player 128-action to 128-player 2-action. Code and data are available at https://github.com/shb20tsinghua/FiberBundle_VI.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.16158",
  "author_total": 1,
  "authors": [
    {
      "name": "Hongbo Sun"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fdqkt904489dy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.16158",
  "fulltext_url": null,
  "id": "fdqkt904489dy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.16158",
  "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",
      "cs.MA"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "1703|Optimization and Variational Analysis"
    ]
  ],
  "openalex": "W7213403999",
  "pdf_url": "https://arxiv.org/pdf/2609.16158",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fdqkt904489dy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:19Z",
      "native_id": "2609.16158",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.16158"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "The fixed-point bundle method over product-of-simplex domains arising from game equilibria",
  "title_text": "The fixed-point bundle method over product-of-simplex domains arising from game equilibria",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:19Z",
  "url": "https://research.draconitic.com/paper/fdqkt904489dy",
  "venue": "arXiv",
  "versions": []
}