Calibrated Agents as Market Makers: Automated Liquidity Provision for Long-Tail Prediction Markets

Calibrated Agents as Market Makers: Automated Liquidity Provision for Long-Tail Prediction Markets | 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 Calibrated Agents as Market Makers: Automated Liquidity Provision for Long-Tail Prediction Markets Nihar Shah This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9339189/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 5 You are reading this latest preprint version Abstract Under what conditions can a forecasting agent profitably provide liquidity on a prediction market? We derive a decomposition of the optimal market-making spread into a microstructure term and an adverse selection term proportional to the agent's mean absolute estimation error~$\alpha$. The profitability condition $s > 2\varphi\alpha$ depends only on the sign of per-fill profit and holds for any positive fill-rate function. A threshold theorem shows that tolerable calibration error increases with existing market spread---a comparative static suggesting that calibrated agents may add the most value on illiquid long-tail markets that lack human market makers. Monte Carlo simulations across 3{,}000 synthetic markets calibrated to empirical Polymarket parameters ($\kappa = 36$) show win rates near 68--70\% across calibration levels, with mean profit varying by $3.4\times$ (\$5.83 to \$1.72), confirming that calibration quality drives profit magnitude. On the empirical side, the main finding is a calibration gap: five frontier LLMs evaluated on 15 resolved Polymarket questions reveal that market-alignment error (MAD $\leq$ 0.029) underestimates true estimation error ($\alpha$ up to 0.437) by an order of magnitude---a result with implications for any system using market prices as calibration targets. The model omits inventory risk and multi-agent competition, limiting direct deployment conclusions, but the spread decomposition provides a tractable framework for analyzing when AI-agent liquidity provision is viable. JEL Classification: D47 , G14 , G17 , C63 prediction markets automated market making LLM calibration adverse selection DeFi liquidity Glosten–Milgrom Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Reviewers agreed at journal 22 Apr, 2026 Reviewers invited by journal 20 Apr, 2026 Editor assigned by journal 13 Apr, 2026 Submission checks completed at journal 13 Apr, 2026 First submitted to journal 07 Apr, 2026 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-9339189","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":622103286,"identity":"127ef2f2-dace-41cf-a237-43dc7a963265","order_by":0,"name":"Nihar Shah","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA30lEQVRIiWNgGAWjYFACHjYQmcAgwXwASEvIkKKFLQGkhYcULTwGYC5BDebsvcce/NxTl8c/u+fzqxs1FjwM7IePbsCnxbLnXLphz7PDxRJ3zm6zzjkGdBhPWtoNfFoMbuSYSfAcOJDYcCN3m3EOG1CLBI8Zfi3335hJ/jlQlzj/Rs4z45x/xGi5wWMmzXOAOXHDjRzmx7ltxGg5k2MmLXPgcOLGG2lmzLl9EjxsBP1y/IyZ5Bugw+bdSH78OedbnRw/++FjeLUgAzYJMEmschBg/kCK6lEwCkbBKBg5AABflUr7rCztpgAAAABJRU5ErkJggg==","orcid":"","institution":"Independent","correspondingAuthor":true,"prefix":"","firstName":"Nihar","middleName":"","lastName":"Shah","suffix":""}],"badges":[],"createdAt":"2026-04-07 04:08:32","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9339189/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9339189/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":106961285,"identity":"afad1bc5-74d2-4c68-8c8f-c9e55fb6a27a","added_by":"auto","created_at":"2026-04-15 09:24:57","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2816721,"visible":true,"origin":"","legend":"","description":"","filename":"niharshahmanuscriptsubmission.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9339189/v1_covered_b36bec23-1fba-4cb4-bef3-b5684f9dd089.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Calibrated Agents as Market Makers: Automated Liquidity\nProvision for Long-Tail Prediction Markets","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":false,"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":"digital-finance","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"dfin","sideBox":"Learn more about [Digital Finance](http://link.springer.com/journal/42521)","snPcode":"42521","submissionUrl":"https://submission.nature.com/new-submission/42521/3","title":"Digital Finance","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"prediction markets, automated market making, LLM calibration, adverse selection, DeFi liquidity, Glosten–Milgrom","lastPublishedDoi":"10.21203/rs.3.rs-9339189/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9339189/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eUnder what conditions can a forecasting agent profitably provide liquidity on a prediction market? We derive a decomposition of the optimal market-making spread into a microstructure term and an adverse selection term proportional to the agent's mean absolute estimation error~$\\alpha$. The profitability condition $s \u0026gt; 2\\varphi\\alpha$ depends only on the sign of per-fill profit and holds for any positive fill-rate function. A threshold theorem shows that tolerable calibration error increases with existing market spread---a comparative static suggesting that calibrated agents may add the most value on illiquid long-tail markets that lack human market makers. Monte Carlo simulations across 3{,}000 synthetic markets calibrated to empirical Polymarket parameters ($\\kappa = 36$) show win rates near 68--70\\% across calibration levels, with mean profit varying by $3.4\\times$ (\\$5.83 to \\$1.72), confirming that calibration quality drives profit magnitude. On the empirical side, the main finding is a calibration gap: five frontier LLMs evaluated on 15 resolved Polymarket questions reveal that market-alignment error (MAD $\\leq$ 0.029) underestimates true estimation error ($\\alpha$ up to 0.437) by an order of magnitude---a result with implications for any system using market prices as calibration targets. The model omits inventory risk and multi-agent competition, limiting direct deployment conclusions, but the spread decomposition provides a tractable framework for analyzing when AI-agent liquidity provision is viable.\u003c/p\u003e\n\u003cp\u003eJEL Classification: D47 , G14 , G17 , C63\u003c/p\u003e","manuscriptTitle":"Calibrated Agents as Market Makers: Automated Liquidity\nProvision for Long-Tail Prediction Markets","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-04-14 13:12:03","doi":"10.21203/rs.3.rs-9339189/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"reviewerAgreed","content":"13063198947476536512937145033870848905","date":"2026-04-22T09:37:07+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-04-20T07:58:30+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-04-13T08:52:38+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2026-04-13T05:45:59+00:00","index":"","fulltext":""},{"type":"submitted","content":"Digital Finance","date":"2026-04-07T04:04:14+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"digital-finance","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"dfin","sideBox":"Learn more about [Digital Finance](http://link.springer.com/journal/42521)","snPcode":"42521","submissionUrl":"https://submission.nature.com/new-submission/42521/3","title":"Digital Finance","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"e145d2a3-1f89-44c2-b030-45d55bda7bda","owner":[],"postedDate":"April 14th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-04-20T08:08:38+00:00","versionOfRecord":[],"versionCreatedAt":"2026-04-14 13:12:03","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9339189","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9339189","identity":"rs-9339189","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}