Spurious Equilibrium in the Graph Model for Conflict Resolution under Catastrophic Risk

Spurious Equilibrium in the Graph Model for Conflict Resolution under Catastrophic Risk | 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 Spurious Equilibrium in the Graph Model for Conflict Resolution under Catastrophic Risk Yukiko Kato This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8587470/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract In many strategic conflicts, certain states represent catastrophic outcomes that must be avoided at all costs.When equilibrium analysis implicitly relies on threats or sanctions that traverse such catastrophic states, the resulting stability predictions may be operationally meaningless.This paper introduces the concept of spurious equilibrium to formalize this phenomenon in the Graph Model for Conflict Resolution (GMCR).A state exhibits spurious stability if its equilibrium status depends essentially on paths through catastrophic states.We provide formal characterizations of spurious equilibria for Nash stability, General Metarationality (GMR), Symmetric Metarationality (SMR), and Sequential Stability (SEQ).Each stability concept admits spurious equilibria under different structural conditions.The characterization theorems clarify when classical equilibrium predictions can be trusted in high-risk environments and provide diagnostic criteria for identifying misleading stability conclusions.Illustrative examples using Prisoner's Dilemma and Chicken Game demonstrate the practical implications of the framework. Graph model for conflict resolution Stability analysis Spurious equilibrium Catastrophic states Metarationality Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted 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. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8587470","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":578556255,"identity":"0ccd56fd-f972-483c-947a-8782b6453ee2","order_by":0,"name":"Yukiko 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