Monotone Inclusion Approach to Weakly Monotone Discrete-Time Finite-Horizon Mean-Field Games

[2608.15079] Monotone Inclusion Approach to Weakly Monotone Discrete-Time Finite-Horizon Mean-Field Games Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Optimization and Control arXiv:2608.15079 (math) [Submitted on 15 Aug 2026] Title: Monotone Inclusion Approach to Weakly Monotone Discrete-Time Finite-Horizon Mean-Field Games Authors: Uğur Aydın , Tamer Başar , Naci Saldi View a PDF of the paper titled Monotone Inclusion Approach to Weakly Monotone Discrete-Time Finite-Horizon Mean-Field Games, by U\u{g}ur Ayd{\i}n and 2 other authors View PDF HTML (experimental) Abstract: We revisit the problem of computing mean-field equilibria (MFEs) in discrete-time, monotone, finite-horizon mean-field games (MFGs). We show that, when the transition kernel is independent of the state-measure term and the reward function satisfies the usual weak monotonicity condition and is Lipschitz continuous, anchored proximal gradient descent methods can be used to compute a monotone MFE. We also establish last-iterate convergence results for these methods. Our approach relies on formulating the computation problem as an optimization problem over the space of occupation measures. Using this formulation, we show that the problem is equivalent to a class of constrained Lipschitz monotone inclusion problems. We then apply iterative methods for this monotone inclusion formulation to derive a tractable algorithm. The resulting algorithm achieves a convergence rate of \(O(1/\sqrt{T})\) after \(T\) iterations, without requiring any regularization. This rate holds even in the absence of a uniqueness assumption for the corresponding MFE. Subjects: Optimization and Control (math.OC) Cite as: arXiv:2608.15079 [math.OC] (or arXiv:2608.15079v1 [math.OC] for this version) https://doi.org/10.48550/arXiv.2608.15079 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Ugur Aydin [ view email ] [v1] Sat, 15 Aug 2026 06:55:52 UTC (100 KB) Full-text links: Access Paper: View a PDF of the paper titled Monotone Inclusion Approach to Weakly Monotone Discrete-Time Finite-Horizon Mean-Field Games, by U\u{g}ur Ayd{\i}n and 2 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.OC < prev | next > new | recent | 2026-08 Change to browse by: math References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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