Generalized model of stochastic common property fishery differential game: Numerical study

Generalized model of stochastic common property fishery differential game: Numerical study | 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 Generalized model of stochastic common property fishery differential game: Numerical study Zahra Nikooeinejad, Mohammad Heydari This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4264035/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 06 Aug, 2025 Read the published version in Dynamic Games and Applications → Version 1 posted 7 You are reading this latest preprint version Abstract In a generalized model of stochastic common property differential game problem, we have a more flexible framework that extends the model to handle the natural growth, price and cost functions for a wide range of parameters. Unlike previous studies that appeared in the literature, instead of keeping the model as parsimonious as possible, we consider the nonlinear resource stock dynamics and nonquadratic payoff functions, focusing on monopoly, duopoly and oligopoly games with a feedback information structure. It is observed that the choice of model parameters has an important influence on the nature and analytical behavior of solution of the nonlinear HJB PDEs (ODEs) and consequently on Nash equilibrium strategies for finite- (infinite-) horizon planning. We can not derive a closed-form solution for this class of generalized models. Hence, this paper presents a collocation method based on the fractional-order shifted Chelyshkov polynomials to solve the nonlinear Hamilton-Jacobi-Bellman PDEs (ODEs) in the generalized stochastic common property differential game problem with finite- (infinite-) horizon. Numerical results show that the choice of different parameters in the approximate solutions based on the fractional-order shifted Chelyshkov polynomials greatly affect the performance of the collocation method. Also, the results show that the firms' optimal extraction plans are strongly influenced by the natural growth, price and cost functions with respect to different parameters. Simulation Stochastic differential games Common property resources Hamilton-Jacobi-Bellman PDE (ODEs) Fractional-order Chelyshkov collocation method Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 06 Aug, 2025 Read the published version in Dynamic Games and Applications → Version 1 posted Editorial decision: Revision requested 13 Sep, 2024 Reviews received at journal 02 Sep, 2024 Reviewers agreed at journal 02 May, 2024 Reviewers invited by journal 23 Apr, 2024 Editor assigned by journal 17 Apr, 2024 Submission checks completed at journal 17 Apr, 2024 First submitted to journal 14 Apr, 2024 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-4264035","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":292466539,"identity":"a82cd48f-24d8-4d51-9dc4-140e2bd93200","order_by":0,"name":"Zahra Nikooeinejad","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABFklEQVRIie2RsWrDMBCGzxg0yZkFdetXkPHQxTT0TSwCngL1FDIEKiioiyGrp/YV7DeQEHgyzgNkaZZOGdotS6BKCSmFKHgsVB/oPw36uDsE4HD8URQ3gcyhgFL4rgY8VMmHKR4/XZE+KVYiHihVzdOb0dWTLHazFVsudQ27BYS3/Lzi8VGm6i5PUNhmcdmvWSXbwitbwKE8r/iAqdoIzQSZUhqINeOqpBBwwMQyGDoqj4I8fMR70bNXjam3v6Dgg9IInSEyhSQQktUtpv6lLsQ3StXlsSA5TcJ+kjQdKnTYEqsSPZfJZzlPo6iavMfb2d31y0o3m+0iHdsUs//PXof/uOcmpGlvE37bbybGg546HA7Hv+ILZOhWsFlMwGUAAAAASUVORK5CYII=","orcid":"","institution":"Yazd University","correspondingAuthor":true,"prefix":"","firstName":"Zahra","middleName":"","lastName":"Nikooeinejad","suffix":""},{"id":292466540,"identity":"db704c41-f929-49e9-8a7f-6fa232cc44a0","order_by":1,"name":"Mohammad Heydari","email":"","orcid":"","institution":"Yazd University","correspondingAuthor":false,"prefix":"","firstName":"Mohammad","middleName":"","lastName":"Heydari","suffix":""}],"badges":[],"createdAt":"2024-04-14 07:48:21","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4264035/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4264035/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s13235-025-00669-9","type":"published","date":"2025-08-06T15:57:58+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":88814987,"identity":"2bcf3dfb-4b58-4f60-b0c4-b4aebadf8abf","added_by":"auto","created_at":"2025-08-11 16:10:23","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1752782,"visible":true,"origin":"","legend":"","description":"","filename":"ManuscriptFCCMforStochasticResouExtFinal.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4264035/v1_covered_7f4e1981-e315-48b6-b9a6-3c0488dc520e.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Generalized model of stochastic common property fishery differential game: Numerical study","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"dynamic-games-and-applications","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"dgaa","sideBox":"Learn more about [Dynamic Games and Applications](http://link.springer.com/journal/13235)","snPcode":"13235","submissionUrl":"https://submission.nature.com/new-submission/13235/3","title":"Dynamic Games and Applications","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Simulation, Stochastic differential games, Common property resources, Hamilton-Jacobi-Bellman PDE (ODEs), Fractional-order Chelyshkov collocation method","lastPublishedDoi":"10.21203/rs.3.rs-4264035/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4264035/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"In a generalized model of stochastic common property differential game problem, we have a more flexible framework that extends the model to handle the natural growth, price and cost functions for a wide range of parameters. 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