Mathematical Framework for ABM-MARL Integration in Financial Systems: A Discrete Multi-Agent Population-Strategy Game Approach

Mathematical Framework for ABM-MARL Integration in Financial Systems: A Discrete Multi-Agent Population-Strategy Game Approach | 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 Mathematical Framework for ABM-MARL Integration in Financial Systems: A Discrete Multi-Agent Population-Strategy Game Approach Bhaktavaschal Samal This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7326746/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 Modern financial markets feature complex interactions between vast populations of rule-based agents and adaptive algorithmic traders, yet existing models treat these layers separately. We introduce a discrete-time population-strategy game unifying Agent-Based Modeling (ABM) and Multi-Agent Reinforcement Learning (MARL) with five core innovations: (1) an asymmetric bilevel architecture where strategic agents optimize over population distributions while endogenously shaping them; (2) heavy-tailed α-stable noise (1 < α ≤ 2) capturing financial returns; (3) endogenous population-type switching with performance feedback; (4) partial observability via aggregated noisy statistics (e.g., order flow); and (5) regulatory-aware equilibria with dynamic feasibility constraints. Under mild conditions, we prove: • Existence of mean-field equilibrium with spectral stability certification (ρ(∇μΦ) < 1) • Almost-sure convergence of two-timescale learning (policy gradient + population dynamics) • O(N^−1/2) finite-population approximation error Our linearly scalable Population-Strategy Policy Gradient (PSPG) algorithm enables tractable computation. Experiments in market making and crisis contagion demonstrate: • Emergent critical thresholds (e.g., 8.2 bps spreads bifurcating stable/fragmented regimes) • 23% volatility reduction versus pure ABM • Robustness to regulatory constraints (MiFID II) and heavy-tailed shocks This framework bridges ABM’s emergent heterogeneity with MARL’s strategic adaptation, addressing key gaps in mean-field games (discrete-time alignment, strategic heterogeneity) and enabling real-world deployment with verifiable stability. Agent-Based Modeling Multi-Agent RL Financial Markets Mean-Field Games Regulatory AI Stochastic Approximation 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. 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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-7326746","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":499983287,"identity":"cadb3254-6804-4539-a737-df2e55549c42","order_by":0,"name":"Bhaktavaschal Samal","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAwElEQVRIiWNgGAWjYBACAwhlIQciDzwgQYuEMVhLAilaEhtAFFFazCXSH366USORPj/s8EOgLXZyug0EtFjOyDGWzjkmkbvxdpoBUEuysdkBQg47c4ZBOocNqGV2AkjLgcRthLUcf/w7559EuuHs9A9EajneYCad2yaRIC+dQ6Qtlu09Zta5fRKGG6RzCg4kGBDhF3Nm9se3c77ZyMvPTt/84UOFnRxBLQgXglUaEKscBOQbSFE9CkbBKBgFIwoAAFQRRIfEJ0VFAAAAAElFTkSuQmCC","orcid":"","institution":"Government of Odisha, India","correspondingAuthor":true,"prefix":"","firstName":"Bhaktavaschal","middleName":"","lastName":"Samal","suffix":""}],"badges":[],"createdAt":"2025-08-08 11:23:22","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7326746/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7326746/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":93065767,"identity":"f72b316d-2525-4bf5-bdad-847a72aea62c","added_by":"auto","created_at":"2025-10-08 16:45:54","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":578326,"visible":true,"origin":"","legend":"","description":"","filename":"MathematicalFrameworkforABMMARLIntegrationinFinancialSystem080820251.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7326746/v1_covered_0a3d0393-f610-4857-aeaa-bf189e88b344.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Mathematical Framework for ABM-MARL Integration in Financial Systems: A Discrete Multi-Agent Population-Strategy Game Approach","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"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":"Agent-Based Modeling, Multi-Agent RL, Financial Markets, Mean-Field Games, Regulatory AI, Stochastic Approximation","lastPublishedDoi":"10.21203/rs.3.rs-7326746/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7326746/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eModern financial markets feature complex interactions between vast populations of rule-based agents and adaptive algorithmic traders, yet existing models treat these layers separately. We introduce a discrete-time population-strategy game unifying Agent-Based Modeling (ABM) and Multi-Agent Reinforcement Learning (MARL) with five core innovations: (1) an asymmetric bilevel architecture where strategic agents optimize over population distributions while endogenously shaping them; (2) heavy-tailed α-stable noise (1 \u0026lt; α ≤ 2) capturing financial returns; (3) endogenous population-type switching with performance feedback; (4) partial observability via aggregated noisy statistics (e.g., order flow); and (5) regulatory-aware equilibria with dynamic feasibility constraints.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eUnder mild conditions, we prove:\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e• Existence of mean-field equilibrium with spectral stability certification (ρ(∇μΦ) \u0026lt; 1)\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e• Almost-sure convergence of two-timescale learning (policy gradient + population dynamics)\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e• O(N^−1/2) finite-population approximation error\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eOur linearly scalable Population-Strategy Policy Gradient (PSPG) algorithm enables tractable computation. Experiments in market making and crisis contagion demonstrate:\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e• Emergent critical thresholds (e.g., 8.2 bps spreads bifurcating stable/fragmented regimes)\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e• 23% volatility reduction versus pure ABM\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e• Robustness to regulatory constraints (MiFID II) and heavy-tailed shocks\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThis framework bridges ABM’s emergent heterogeneity with MARL’s strategic adaptation, addressing key gaps in mean-field games (discrete-time alignment, strategic heterogeneity) and enabling real-world deployment with verifiable stability.\u003c/p\u003e","manuscriptTitle":"Mathematical Framework for ABM-MARL Integration in Financial Systems: A Discrete Multi-Agent Population-Strategy Game Approach","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-08-14 07:35:56","doi":"10.21203/rs.3.rs-7326746/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","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}}],"origin":"","ownerIdentity":"c5b732bd-ba63-49b1-9178-67249c26c2a2","owner":[],"postedDate":"August 14th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-10-08T16:43:10+00:00","versionOfRecord":[],"versionCreatedAt":"2025-08-14 07:35:56","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7326746","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7326746","identity":"rs-7326746","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}