Endogenous Networks, Pricing Strategies, and State Regulation in Oligopolistic Markets: A Three-Stage Model with Eigenvector Centrality

Endogenous Networks, Pricing Strategies, and State Regulation in Oligopolistic Markets: A Three-Stage Model with Eigenvector Centrality | 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 Endogenous Networks, Pricing Strategies, and State Regulation in Oligopolistic Markets: A Three-Stage Model with Eigenvector Centrality Balázs Szabó, Zsolt Nemeskéri This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6930926/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 This study presents a game-theoretic model of oligopolistic competition in digital markets, integrating endogenous network formation, varied pricing strategies, nonlinear demand, network externalities, and state regulation to analyze price differences. The model features a three-stage game where the state implements taxes and subsidies to maximize social welfare, producers invest in network connections, and set prices, some using consumer connection-based pricing. Consumers form connections based on prices, investments, and state incentives, creating scale-free networks. Through advanced mathematical methods, we prove a stable equilibrium, linking prices to a measure of network influence shaped by regulation. Simulations across various network structures, including a large-scale case with 50 producers, show that baseline regulation reduces price differences by about 28 % and increases welfare by up to 12 %. Further analysis reveals that stronger taxes and subsidies further decrease price variation by approximately 77 % and boost welfare by 15 %, guiding regulatory design. Aligned with the European Union’s Digital Markets Act and United States antitrust actions, this model provides strategic and policy insights for platform economies, advancing industrial organization and competition policy research. JEL: C72, D43, D85, L13, L51 Oligopolistic competition Endogenous networks Price heterogeneity Eigen-vector centrality State regulation Network externalities Nonlinear demand 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-6930926","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":473594966,"identity":"db445e23-8e26-49a0-a4e3-476f66ba5d46","order_by":0,"name":"Balázs Szabó","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA3klEQVRIiWNgGAWjYHACNiA+wMAHYn4AERLEagGRjDMYDEjUwsxDjBb5/sPPHnxguCPPxn788WfbHX/kGKR7DPBqMThwzNxwBsMzwzaehDTp3DMGxgwyZwhoYWwwk+ZhOMzYxpBwjDm3zSCxQSIHvxb5ZvZvIC32bfwPmz9bthnUE9TCcIwHbEtim0QygzRjm0ECAyEtBmd4yg1nGDxLbpN4xibZe8bYsE0irQC/w/qPb3vwoeKObT9/+uMPP3fIyfNLJG/A7zCIXVCasQESTSQAkJZRMApGwSgYBegAAEV7QHXNrkxPAAAAAElFTkSuQmCC","orcid":"","institution":"University of Pecs","correspondingAuthor":true,"prefix":"","firstName":"Balázs","middleName":"","lastName":"Szabó","suffix":""},{"id":473594967,"identity":"df82366a-82f3-4ed1-8137-e69f71f08461","order_by":1,"name":"Zsolt Nemeskéri","email":"","orcid":"","institution":"University of Pecs","correspondingAuthor":false,"prefix":"","firstName":"Zsolt","middleName":"","lastName":"Nemeskéri","suffix":""}],"badges":[],"createdAt":"2025-06-19 11:53:18","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6930926/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6930926/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":85325446,"identity":"3d7f3087-273a-4255-b852-37448eb07b9d","added_by":"auto","created_at":"2025-06-24 16:23:38","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":617397,"visible":true,"origin":"","legend":"","description":"","filename":"NetPricingState.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6930926/v1_covered_f5cab270-9c2c-469b-97e6-1026f5846db6.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Endogenous Networks, Pricing Strategies, and State Regulation in Oligopolistic Markets: A Three-Stage Model with Eigenvector Centrality","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":"Oligopolistic competition, Endogenous networks, Price heterogeneity, Eigen-vector centrality, State regulation, Network externalities, Nonlinear demand","lastPublishedDoi":"10.21203/rs.3.rs-6930926/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6930926/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis study presents a game-theoretic model of oligopolistic competition in digital markets, integrating endogenous network formation, varied pricing strategies, nonlinear demand, network externalities, and state regulation to analyze price differences. 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