Partial Cooperation, Spatial Agglomeration, and Heterogeneity of Firms in a Horizontal and Vertical Differentiation

Partial Cooperation, Spatial Agglomeration, and Heterogeneity of Firms in a Horizontal and Vertical Differentiation | 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 Partial Cooperation, Spatial Agglomeration, and Heterogeneity of Firms in a Horizontal and Vertical Differentiation Tai-Liang Chen, Fengning Huan This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3907665/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 paper constructs a horizontally and vertically differentiated product model in a repeated, collusive pricing game. Based upon different profit-sharing rules, it examines the interacting effects of (vertical) quality distortion and cost difference on (horizontal) market competition. It shows that the asymmetry between marginal cost and perceived quality matters for the emergence of agglomeration. If the magnitude of cost differentials between firms is equal to the magnitude of quality difference, minimal horizontal differentiation emerges in each period regardless of the order of moves and profit-sharing rules. If the magnitudes of cost and quality differences differ, non-minimal horizontal differentiation emerges in each period in a simultaneous-move game. In a sequential-move game, the second-mover advantage exists if the second mover’s strong suit dominates the first mover’s one. Spatial agglomeration/minimal differentiation emerges when the second mover chooses the same location as the first mover under profit maximization. The heterogeneity creates a conflict of interest between firms. Hence, agglomeration appears with the heterogeneity of firms under certain conditions in equilibrium. JEL classification : C70, D43, L11, R12 Partial collusion/parallel pricing Repeated Bertrand game Spatial agglomeration Cost asymmetry Quality differentiation 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-3907665","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":269794918,"identity":"cd93fa94-d5fb-4c33-a330-3661401de357","order_by":0,"name":"Tai-Liang Chen","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABDklEQVRIiWNgGAWjYFACxsYDCWAGDxBXADE7lI0L8DAwNiBpOQPEzAS1MDAcgDMZ24jQYs9+uOHAg5o7dg3sZw8+LpxXl9jPzMD44G0bg7w5Llt4EoEOO/YsuYEnL9l45ja2xJnNDMyGc9sYDHc24HIYSAvb4WQGCR4zad5tPIkbDjOwSfO2MSQYHMChhf8hUMs/sBbz37xzJBL3H2Zg/41XiwTQlsS2w3YgW5h5GwwSNzAzsDHj1XIDaEti3+EENp4cY2meYwnGMw4zNkvOOSdhuAGHFvb+9IcPf3w7bM/PfsbwM09NnWx/e/PBD2/KbORx2QIDiW0INmMDkJDArx4I7AmqGAWjYBSMgpELAEG0VxRJq4EcAAAAAElFTkSuQmCC","orcid":"","institution":"Zhongnan University of Economics and Law","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Tai-Liang","middleName":"","lastName":"Chen","suffix":""},{"id":269794919,"identity":"181a8092-b6da-4d08-abb1-942d02a4eb83","order_by":1,"name":"Fengning Huan","email":"","orcid":"","institution":"Nankai University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Fengning","middleName":"","lastName":"Huan","suffix":""}],"badges":[],"createdAt":"2024-01-29 03:00:31","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3907665/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3907665/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":53689072,"identity":"871f8619-fe26-4214-91ed-06d3f3e6749b","added_by":"auto","created_at":"2024-03-29 01:07:45","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":473549,"visible":true,"origin":"","legend":"","description":"","filename":"240128ChenHuanfullmanuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3907665/v1_covered_1e989140-bdbc-421a-9272-54afeffcd8c3.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Partial Cooperation, Spatial Agglomeration, and Heterogeneity of Firms in a Horizontal and Vertical Differentiation","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":"Partial collusion/parallel pricing, Repeated Bertrand game, Spatial agglomeration, Cost asymmetry, Quality differentiation","lastPublishedDoi":"10.21203/rs.3.rs-3907665/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3907665/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis paper constructs a horizontally and vertically differentiated product model in a repeated, collusive pricing game. 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