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The fixed-point bundle method over product-of-simplex domains arising from game equilibria — arXiv:2609.16158

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.16158
License (as archived): CC0-1.0
Archived: 2026-10-15T18:31:18.315Z
SHA-256 of the archived text: fe53accb797a93c06999934a929f89e3166ef70388d8af842544678e09fd6816
Stable URL of this page: https://metraipolis.com/documento/dc_bd71bbc4cc90

How to cite

The fixed-point bundle method over product-of-simplex domains arising from game equilibria — arXiv:2609.16158 — arXiv (en), https://arxiv.org/abs/2609.16158 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_bd71bbc4cc90 (Metraipolis archive dc_bd71bbc4cc90, sha256 fe53accb797a93c06999934a929f89e3166ef70388d8af842544678e09fd6816)

BibTeX

@misc{dcbd71bbc4cc90,
  title = {The fixed-point bundle method over product-of-simplex domains arising from game equilibria — arXiv:2609.16158},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.16158},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_bd71bbc4cc90; sha256 fe53accb797a93c06999934a929f89e3166ef70388d8af842544678e09fd6816},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.16158. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

This paper extends the fixed-point bundle framework for finite-dimensional variational inequalities (VIs) from the simplex domain to the product-of-simplex domain, which is directly applicable to solving Nash equilibria. The fixed-point bundle for VIs on the product-of-simplex domain reveals a composite fiber bundle structure. The key innovation is to construct an equivalent VI on the simplex domain and establish the equivalence between the two fixed-point bundle frameworks via a fiber bundle isomorphism. Exploiting this geometric equivalence, the predictor-corrector path-following algorithm for the VI on the product-of-simplex domain is shown to inherit the convergence guarantee of the simplex-domain framework, namely, global convergence with linear gap reduction near solutions. Numerical experiments on 5600 randomly generated instances with dimensions ranging from 2-player 128-action to 128-player 2-action demonstrate robust performance. The algorithm converges in every tested instance.

Tema degli esploratori: agenti e intelligenza artificiale (retro-catalogo arXiv: annunci del 2026-09-16 in cs.MA).
Categorie arXiv: Optimization and Control (math.OC) ; Computer Science and Game Theory (cs.GT); Multiagent Systems (cs.MA).
Pagina del lavoro: https://arxiv.org/abs/2609.16158 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-15T18:00:46.644Z dalla pagina https://arxiv.org/catchup/cs.MA/2026-09-16?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).