Sequential Decomposition of Correlated Mean-Field Games

Sequential Decomposition of Correlated Mean-Field Games | 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 Sequential Decomposition of Correlated Mean-Field Games Abhishek Shende, Deepanshu Vasal This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7794020/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 this paper, we study \emph{mean-field correlated equilibria} (MFCE), a class of correlated equilibria in mean-field games (MFGs) that enables decentralized coordination through a shared correlation device. Unlike standard mean-field equilibria (MFE), where agents act independently, MFCE allows agents to receive statistically correlated strategy recommendations, improving efficiency and fairness without direct communication. Using a sequential decomposition approach, we provide a backward-recursive characterization of MFCE for finite-horizon discrete-time games. The recursion incorporates incentive compatibility constraints, ensuring that no agent benefits from deviating from the recommended strategies while maintaining mean-field consistency. We illustrate MFCE through numerical examples a public investment game with heterogeneous costs. In both cases, MFCE achieves higher social efficiency, better steady-state outcomes, and increased continuation values for high-cost or high-risk agents compared to MFE. Our results establish MFCE as a tractable and conceptually meaningful extension of MFE, offering a practical framework for coordinating large populations of decentralized agents in settings where independent strategies are inefficient. Mean Field Games Correlated equilibrium restricted strategy Sequential Decomposition 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. 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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-7794020","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":530500586,"identity":"98de2ada-8d87-4dfb-932e-9fb329a99cd7","order_by":0,"name":"Abhishek Shende","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA4ElEQVRIiWNgGAWjYDACCR6Ggw0MDDL8DIcPgLgyRGvhkWw8lgDhEqOFEaTF4PAZAxCfsBb+2b0HD86osOExOHbm86sbNRY8DOyHj27Aa8mdcwkHN5xJ45E8c3abdc4xoKU8aWk38FpzI8fg4MO2wzx8N85uM85hA2qR4DHDq0UepoXh/ptnxjn/iNBiANKyEahF4MAZ5se5bURoMbxzxuDgDJBfGo6ZMef2SfCwEfKL3O0e4489FTZywKh8/DnnW50cP/vhY/i9jwTYJMAkscpBgPkDKapHwSgYBaNg5AAAMFxQxSOxINEAAAAASUVORK5CYII=","orcid":"","institution":"The University of Texas at Austin","correspondingAuthor":true,"prefix":"","firstName":"Abhishek","middleName":"","lastName":"Shende","suffix":""},{"id":530500587,"identity":"f4d837cb-aad1-444a-be23-36bfdf82d1a4","order_by":1,"name":"Deepanshu Vasal","email":"","orcid":"","institution":"Northwestern University","correspondingAuthor":false,"prefix":"","firstName":"Deepanshu","middleName":"","lastName":"Vasal","suffix":""}],"badges":[],"createdAt":"2025-10-06 19:53:18","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7794020/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7794020/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":94400612,"identity":"3afce712-40df-433e-9722-de79bf8169df","added_by":"auto","created_at":"2025-10-27 13:58:19","extension":"json","order_by":0,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":3854,"visible":true,"origin":"","legend":"","description":"","filename":"72470b6bc9e44f94b4ad4a6c85a40d77.json","url":"https://assets-eu.researchsquare.com/files/rs-7794020/v1/f80f542f7bb882cff5adc537.json"},{"id":102297575,"identity":"51d7a434-7481-45f1-ac9b-5b52adfcbaf3","added_by":"auto","created_at":"2026-02-10 10:28:19","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":539116,"visible":true,"origin":"","legend":"","description":"","filename":"MFCEDynamicGamesandApplications2.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7794020/v1_covered_ec72ad6c-32aa-44d8-8413-6de768ce7bd7.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Sequential Decomposition of Correlated Mean-Field Games","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Mean Field Games, Correlated equilibrium, restricted strategy, Sequential Decomposition","lastPublishedDoi":"10.21203/rs.3.rs-7794020/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7794020/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"In this paper, we study \\emph{mean-field correlated equilibria} (MFCE), a class of correlated equilibria in mean-field games (MFGs) that enables decentralized coordination through a shared correlation device. 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