Graphon Design for Human-Machine Coordination under Bounded Rationality: Optimality of Stochastic Block Models

[2608.27851] Graphon Design for Human-Machine Coordination under Bounded Rationality: Optimality of Stochastic Block Models Skip to main content Search Submit Donate Log in Electrical Engineering and Systems Science > Systems and Control arXiv:2608.27851 (eess) [Submitted on 28 Aug 2026] Title: Graphon Design for Human-Machine Coordination under Bounded Rationality: Optimality of Stochastic Block Models Authors: Zhewei Wang , Vu Anh Phi , Marcos M. Vasconcelos View PDF HTML (experimental) Abstract: Coordination is a desirable feature in multi-agent systems, ranging from robotic swarms to socioeconomic networks. This paper is concerned with promoting coordination among heterogeneous agents, e.g., machines and humans, interacting in a stag-hunt game. In our model the agents exhibit bounded rationality at different levels, which leads to uncertainty and a propensity for errors during learning and decision-making processes. This paper addresses the problem of designing a network topology that maximizes a global metric of coordination under such constraints. While optimizing over the discrete space of finite graphs is generally computationally intractable, we employ a mean-field approach to lift the problem into the space of graphons. Within this framework, we analyze agents following a logit learning dynamics. Using calculus of variations, we show that for systems with a bimodal rationality profile, it suffices to search for optimal graphons in the ensemble of stochastic block models. We then propose a water-filling algorithm to find a locally optimal graphon. Finite graphs can then be sampled from the optimized graphon, bypassing the inherent combinatorial complexities of discrete graph optimization. Comments: Accepted for presentation at the IEEE Conference on Decision and Control 2026 Subjects: Systems and Control (eess.SY) ; Computer Science and Game Theory (cs.GT) Cite as: arXiv:2608.27851 [eess.SY] (or arXiv:2608.27851v1 [eess.SY] for this version) https://doi.org/10.48550/arXiv.2608.27851 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Marcos M. Vasconcelos [ view email ] [v1] Fri, 28 Aug 2026 02:41:48 UTC (334 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.GT 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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