Nonlinear Dynamics in 2-Population Mean Field Games Competing for a Resource: Influence on the Tragedy of the Commons

Nonlinear Dynamics in 2-Population Mean Field Games Competing for a Resource: Influence on the Tragedy of the Commons | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Nonlinear Dynamics in 2-Population Mean Field Games Competing for a Resource: Influence on the Tragedy of the Commons Robert A. Brown This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9170221/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 6 You are reading this latest preprint version Abstract Mean field Game (MFG) Theory derived by combining stochastic optimal control with a statistical description of multiple populations of competing agents is increasingly used in many applications, especially those involving acquisition of a resource. Using an ergodic, 2-population MFG model it is demonstrated that nonlinear dynamics caused by the model’s underlying bifurcation structure can dominate predictions as the influence of the optimal control is enhanced by lowering the stochastic diffusivity σ. Multiple ergodic states are predicted, and rapid segregation of the distributions is observed over small ranges of σ close to bifurcation points. Introducing bias toward agents with more expertise breaks the bifurcation structure, however the effects of the bifurcations persist in the resulting multiple disconnected states. Including a common resource that is self-regenerating models the Tragedy of the Commons (TOTC) where the resource is depleted by over-acquisition by the competing populations. The dependence of the TOTC limit on σ and the regeneration rate ( R N ) exhibits the residual influence of the bifurcation structure and controls the sensitivity of the limiting value of R N . Large differences in the maximum resource acquisition between the two populations are predicted. Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Reviews received at journal 14 May, 2026 Reviewers agreed at journal 30 Mar, 2026 Reviewers invited by journal 26 Mar, 2026 Editor assigned by journal 20 Mar, 2026 Submission checks completed at journal 20 Mar, 2026 First submitted to journal 19 Mar, 2026 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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