How Does Misperception Affect Zero-Determinant Strategies In Iterated Prisoner’s Dilemma?

How Does Misperception Affect Zero-Determinant Strategies In Iterated Prisoner’s Dilemma? | 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 How Does Misperception Affect Zero-Determinant Strategies In Iterated Prisoner’s Dilemma? Zhaoyang Cheng, Guanpu Chen, Yiguang Hong This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-1166862/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 8 You are reading this latest preprint version Abstract Zero-determinant (ZD) strategies have attracted wide attention in Iterated Prisoner’s Dilemma (IPD) games, since the player equipped with ZD strategies can unilaterally enforce the two players’ expected utilities subjected to a linear relation. On the other hand, uncertainties, which may be caused by misperception, occur in IPD inevitably in practical circumstances. To better understand the situation, we consider the influence of misperception on ZD strategies in IPD, where the two players, player X and player Y , have different cognitions, but player X detects the misperception and it is believed to make ZD strategies by player Y. We provide a necessary and sufficient condition for the ZD strategies in IPD with misperception, where there is also a linear relationship between players’ utilities in player X’s cognition. Then we explore bounds of players’ expected utility deviation from a linear relationship in player X’s cognition with also improving its own utility. Computational Mathematics Applied Mathematics strategies utilities misperception cognition Full Text Additional Declarations No competing interests reported. Supplementary Files SI.pdf Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Major revision 06 Jan, 2022 Reviews received at journal 28 Dec, 2021 Reviewers agreed at journal 20 Dec, 2021 Reviewers invited by journal 20 Dec, 2021 Editor assigned by journal 20 Dec, 2021 Editor invited by journal 20 Dec, 2021 Submission checks completed at journal 20 Dec, 2021 First submitted to journal 13 Dec, 2021 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-1166862","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":71454677,"identity":"f61be0f1-8fcc-4cda-9489-6e8586adfe75","order_by":0,"name":"Zhaoyang Cheng","email":"","orcid":"","institution":"Academy of Mathematics and Systems Science, Beijing","correspondingAuthor":false,"prefix":"","firstName":"Zhaoyang","middleName":"","lastName":"Cheng","suffix":""},{"id":71454678,"identity":"e4f0bad3-eccc-4541-bd7d-853ffa4dd8b3","order_by":1,"name":"Guanpu Chen","email":"","orcid":"","institution":"Academy of Mathematics and Systems Science, Beijing","correspondingAuthor":false,"prefix":"","firstName":"Guanpu","middleName":"","lastName":"Chen","suffix":""},{"id":71454679,"identity":"64341fa0-a48f-481d-8295-934cf5e91a32","order_by":2,"name":"Yiguang Hong","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAuUlEQVRIiWNgGAWjYFACHhBhw0OyljTStRwmQYPB+bUHHxf8Oi8j33+A8cMPBrs8wlpuvEs2ntl3m8fgRgKzZA9DcjERWs6YSfP2ALVIMDBIMzAcSGwgUss5HqDDmH8Tp+V8j5k0z48DPAwHEtiIs0XyBo+xMW9DMtAviW2WPQbJhLXwnT9j+Jjnj529fP/hwzd+VNgR1qJwI4GBgbENxGQEKjYgpB4IgL4Gkn+IUDkKRsEoGAUjFwAAiuU8BDecGtwAAAAASUVORK5CYII=","orcid":"","institution":"Tongji University","correspondingAuthor":true,"prefix":"","firstName":"Yiguang","middleName":"","lastName":"Hong","suffix":""}],"badges":[],"createdAt":"2021-12-13 13:59:10","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-1166862/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-1166862/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":16690504,"identity":"51d1ea8b-995a-4415-8e26-a3383f801c34","added_by":"auto","created_at":"2021-12-22 15:43:26","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":371581,"visible":true,"origin":"","legend":"","description":"","filename":"main.pdf","url":"https://assets-eu.researchsquare.com/files/rs-1166862/v1_covered.pdf"},{"id":16690461,"identity":"9fd89c7f-2176-4174-ba31-0cbd77d51a1d","added_by":"auto","created_at":"2021-12-22 15:43:15","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":135711,"visible":true,"origin":"","legend":"","description":"","filename":"SI.pdf","url":"https://assets-eu.researchsquare.com/files/rs-1166862/v1/c34d23f553a12188f8dad892.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"\u003cp\u003eHow Does Misperception Affect Zero-Determinant Strategies In Iterated Prisoner’s Dilemma?\u003c/p\u003e","fulltext":[{"header":"Full Text","content":"This preprint is available for \u003ca href='/article/rs-1166862/latest.pdf' target='_blank'\u003edownload as a PDF\u003c/a\u003e."}],"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":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"strategies, utilities, misperception, cognition","lastPublishedDoi":"10.21203/rs.3.rs-1166862/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-1166862/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Zero-determinant (ZD) strategies have attracted wide attention in Iterated Prisoner’s Dilemma (IPD) games, since the player equipped with ZD strategies can unilaterally enforce the two players’ expected utilities subjected to a linear relation. 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