{"paper":{"title":"The Privacy Subsidy: Kyle's $\\lambda$ under Noise-Perturbed Order-Flow Observation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"In a Kyle model with Gaussian privacy noise added to order flow, the price-impact coefficient and informed-trader strategy rescale by the same factor so their product stays fixed and a closed-form per-period transfer arises from the LP pool","cross_cats":["cs.CR","math.PR","q-fin.TR"],"primary_cat":"cs.GT","authors_text":"Yuki Nakamura","submitted_at":"2026-05-15T08:56:16Z","abstract_excerpt":"Privacy-preserving cryptocurrency exchanges (shielded AMMs, batched swap auctions, sealed-bid order-flow auctions) alter what the pricing mechanism observes about order flow. We derive the unique linear Kyle equilibrium when a committed Bayesian market maker observes order flow perturbed by independent Gaussian privacy noise. The price-impact coefficient and informed-trader strategy both rescale by a single factor in the privacy parameter, and their product is invariant. A welfare decomposition then identifies a closed-form per-period transfer from the protocol's LP pool to traders -- the \"pri"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"The price-impact coefficient and informed-trader strategy both rescale by a single factor in the privacy parameter, and their product is invariant. A welfare decomposition then identifies a closed-form per-period transfer from the protocol's LP pool to traders -- the privacy subsidy.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The market maker is a committed Bayesian observer of order flow that has been perturbed by independent Gaussian privacy noise, and that a unique linear equilibrium exists under this observation model.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Derives closed-form rescaling of Kyle lambda and informed strategy under Gaussian order-flow noise, with invariant product and explicit privacy subsidy from liquidity providers to traders.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"In a Kyle model with Gaussian privacy noise added to order flow, the price-impact coefficient and informed-trader strategy rescale by the same factor so their product stays fixed and a closed-form per-period transfer arises from the LP pool","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"c56e51fd07a64fe2f65194aaee76b41686ddc92b12762b062226adbc9f62c9f2"},"source":{"id":"2605.15746","kind":"arxiv","version":1},"verdict":{"id":"24575eba-88ef-42f0-a73e-070b8b2c7e75","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T18:57:29.309275Z","strongest_claim":"The price-impact coefficient and informed-trader strategy both rescale by a single factor in the privacy parameter, and their product is invariant. A welfare decomposition then identifies a closed-form per-period transfer from the protocol's LP pool to traders -- the privacy subsidy.","one_line_summary":"Derives closed-form rescaling of Kyle lambda and informed strategy under Gaussian order-flow noise, with invariant product and explicit privacy subsidy from liquidity providers to traders.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The market maker is a committed Bayesian observer of order flow that has been perturbed by independent Gaussian privacy noise, and that a unique linear equilibrium exists under this observation model.","pith_extraction_headline":"In a Kyle model with Gaussian privacy noise added to order flow, the price-impact coefficient and informed-trader strategy rescale by the same factor so their product stays fixed and a closed-form per-period transfer arises from the LP pool"},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.15746/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-19T19:33:23.451490Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-19T19:31:19.110336Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T19:12:36.102217Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T17:21:55.974361Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"24a0c21a909f1b7432b6765494259ae14afcefffcc214cb2b976f4a04b300dc6"},"references":{"count":17,"sample":[{"doi":"","year":1908,"title":"arXiv preprint arXiv:1908.08777 (2019)","work_id":"3e04c0ec-e275-449d-95fe-0971e24fa59c","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2024,"title":"https: //whitepaper.renegade.fi/(2024), accessed 2026-05-15","work_id":"2588970a-6948-4516-8d12-610f6aa8b925","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2019,"title":"Journal of Economic Literature57(1), 44–95 (2019)","work_id":"4823ebe7-c0c7-4bca-aa8f-140073cf5eec","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2025,"title":"arXiv preprint arXiv:2501.16488 (2025)","work_id":"6185b13f-8f1d-4555-bf91-bdd24438872a","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2012,"title":"In: Proceedings of the ACM Conference on Electronic Commerce (2012)","work_id":"9f1db88c-f74c-4862-9f6c-ceaefa9f8da9","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":17,"snapshot_sha256":"b635a79c5e6013bb4ce3e10d9e12aa8c4b2926e172a23c800803f03b2827c68b","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"343dda96d4861bb5daf5ba1b02363cd5efcce4b3504f8db366e4e933dc1d2bce"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}