Linear-quadratic mixed Stackelberg-zero-sum game for mean-field regime switching system

[2603.27208] Linear-quadratic mixed Stackelberg-zero-sum game for mean-field regime switching system Skip to main content Search Submit Donate Log in Mathematics > Optimization and Control arXiv:2603.27208 (math) [Submitted on 28 Mar 2026 ( v1 ), last revised 27 Aug 2026 (this version, v2)] Title: Linear-quadratic mixed Stackelberg-zero-sum game for mean-field regime switching system Authors: Pengyan Huang , Na Li , Zuo Quan Xu , Harry Zheng View PDF HTML (experimental) Abstract: Motivated by a green finance problem, a linear-quadratic Stackelberg differential game for a regime switching system involving one leader and two followers is studied. The two followers engage in a zero-sum differential game, and both the state system and the cost functional incorporate a conditional mean-field term. Applying continuation method and induction method, we first establish the existence and uniqueness of the conditional mean-field forward-backward stochastic differential equations with Markovian switching. Based on it, we prove the unique solvability of Hamiltonian systems associated with the two followers and the leader. Moreover, utilizing stochastic maximum principle, decoupling approach and optimal filtering technique, we obtain the optimal feedback strategies for the two followers and the leader. Employing the theoretical results, we solve the green finance problem with some numerical simulations. Subjects: Optimization and Control (math.OC) Cite as: arXiv:2603.27208 [math.OC] (or arXiv:2603.27208v2 [math.OC] for this version) https://doi.org/10.48550/arXiv.2603.27208 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Pengyan Huang [ view email ] [v1] Sat, 28 Mar 2026 09:49:45 UTC (190 KB) [v2] Thu, 27 Aug 2026 09:04:44 UTC (336 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.OC < prev | next > new | recent | 2026-03 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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