Competitive One-Step-Ahead Control of Friedkin--Johnsen Networks: Potential Games, Stability, and the Price of Competition

[2608.27623] Competitive One-Step-Ahead Control of Friedkin--Johnsen Networks: Potential Games, Stability, and the Price of Competition Skip to main content Search Submit Donate Log in Electrical Engineering and Systems Science > Systems and Control arXiv:2608.27623 (eess) [Submitted on 27 Aug 2026] Title: Competitive One-Step-Ahead Control of Friedkin--Johnsen Networks: Potential Games, Stability, and the Price of Competition Authors: Gabriel Gentil , Amit Bhaya View PDF HTML (experimental) Abstract: This paper studies competitive one-step-ahead control of Friedkin-Johnsen networks with overlapping player influence. The one-step interaction is an exact potential game with a unique Nash equilibrium obtained from a symmetric positive-definite system. Sequential best-response sweeps converge for every frozen network state, parallel sweeps obey an exact Jacobi condition (and always converge with two players), and one-sweep implementations require an augmented state-action stability test. For marginal networks, a signed left-right damping condition is sufficient for exact-equilibrium stability and becomes a sharp first-order instability test when its sign is reversed. A resolvent identity clarifies the feedback geometry, while a control-aware centrality identifies the goal conflicts that matter most. We characterize attainable equilibria under unconstrained, convex, and sparse goal restrictions and give a closed form for the same-state welfare loss caused by competition. Numerical examples verify the stability thresholds, geometry, and welfare predictions. Comments: 11 pages, 2 figures. Submitted to IEEE Transactions on Control of Network Systems Subjects: Systems and Control (eess.SY) Cite as: arXiv:2608.27623 [eess.SY] (or arXiv:2608.27623v1 [eess.SY] for this version) https://doi.org/10.48550/arXiv.2608.27623 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Amit Bhaya [ view email ] [v1] Thu, 27 Aug 2026 19:04:13 UTC (125 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: eess.SY < prev | next > new | recent | 2026-08 Change to browse by: cs cs.SY eess 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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