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Extended Graphon Mean-Field Games in Discrete Time — arXiv:2609.04737

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.04737
License (as archived): CC0-1.0
Archived: 2026-10-16T23:11:27.116Z
SHA-256 of the archived text: e15db22039151e2d298ff9174e7eca4810dc1d0f4088a2bcec7ef7e3694861c7
Stable URL of this page: https://metraipolis.com/documento/dc_4e76cd8ac093

How to cite

Extended Graphon Mean-Field Games in Discrete Time — arXiv:2609.04737 — arXiv (en), https://arxiv.org/abs/2609.04737 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_4e76cd8ac093 (Metraipolis archive dc_4e76cd8ac093, sha256 e15db22039151e2d298ff9174e7eca4810dc1d0f4088a2bcec7ef7e3694861c7)

BibTeX

@misc{dc4e76cd8ac093,
  title = {Extended Graphon Mean-Field Games in Discrete Time — arXiv:2609.04737},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.04737},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_4e76cd8ac093; sha256 e15db22039151e2d298ff9174e7eca4810dc1d0f4088a2bcec7ef7e3694861c7},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.04737. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

In this paper, we study games involving a continuum of heterogeneous players in the discrete-time setting with finite state spaces and continuous action spaces. We introduce a new model that incorporates joint state-action interactions within the graphon-weighted aggregate, described by a coupled forward-backward system. We establish the existence of graphon mean-field equilibria and characterize them through this forward-backward system. Additionally, we provide uniqueness results under monotonicity and contraction conditions. To illustrate the practical relevance of our framework, we solve an example of portfolio liquidation with price impact. We provide numerical results for three different graphons and two different initial distributions, illustrating the impact of the network's structure and the distribution heterogeneity on the distribution and the policy.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-07 in math.OC).
Categorie arXiv: Optimization and Control (math.OC).
Pagina del lavoro: https://arxiv.org/abs/2609.04737 — 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 2026-10-16T22:51:59.419Z dalla pagina https://arxiv.org/catchup/math.OC/2026-09-07?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).