Homogenization and Mean-Field Approximation for Multi-Player Games

[2502.12389] Homogenization and Mean-Field Approximation for Multi-Player Games Skip to main content Search Submit Donate Log in Mathematics > Optimization and Control arXiv:2502.12389 (math) [Submitted on 17 Feb 2025 ( v1 ), last revised 27 Aug 2026 (this version, v2)] Title: Homogenization and Mean-Field Approximation for Multi-Player Games Authors: Rama Cont , Anran Hu View PDF Abstract: We investigate how the framework of mean-field games may be used to study strategic interactions in large heterogeneous populations. Starting from a partition of the player population into groups, we introduce an intermediate finite-player game of mean-field type and derive explicit non-asymptotic bounds for the average exploitability of strategy profiles obtained by lifting strategies from the associated multi-population mean-field game. The approximation error decomposes into two components: a finite-population mean-field error, controlled by empirical-measure approximation within each group, and a heterogeneity error measuring deviations of the original players' rewards and transition dynamics from their group-level approximations. Our results apply to compact state and action spaces and allow heterogeneous deterministic initial states within each population. We further study the resulting trade-off between group size and intra-group heterogeneity. In a parametrized heterogeneous setting, the choice of partition minimizing the resulting certified upper bound can be formulated as a mixed-integer second-order cone program. In the large-population regime, this problem is shown to be related to $K$-means clustering. Comments: Revised version: Aug 2026. 35 pages, 1 figure Subjects: Optimization and Control (math.OC) MSC classes: 49N80, 91A06, 91A10, 91A16, 91A15, 91A25, 91A50 Cite as: arXiv:2502.12389 [math.OC] (or arXiv:2502.12389v2 [math.OC] for this version) https://doi.org/10.48550/arXiv.2502.12389 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Rama Cont [ view email ] [v1] Mon, 17 Feb 2025 23:54:50 UTC (65 KB) [v2] Thu, 27 Aug 2026 08:13:11 UTC (41 KB) Full-text links: Access Paper: View PDF TeX Source view license Current browse context: math.OC < prev | next > new | recent | 2025-02 Change to browse by: math References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation 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)

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