{"paper":{"title":"The Privacy Subsidy in Glosten-Milgrom: Bid-Ask Spread and Welfare under Flip-Noise Direction Observation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CR","math.PR","q-fin.TR"],"primary_cat":"cs.GT","authors_text":"Yuki Nakamura","submitted_at":"2026-05-19T12:12:01Z","abstract_excerpt":"We derive a closed-form bid-ask spread and welfare decomposition for the Glosten-Milgrom 1985 sequential-trading model when the market maker observes the trade direction perturbed by a binary flip channel of probability $\\eta$ -- a natural information-theoretic model of privacy mechanisms acting on the direction signal. Under a committed Bayesian market-maker pricing rule, the equilibrium spread is $\\mu(1-2\\eta)\\Delta$, where $\\mu$ is the informed-trader fraction and $\\Delta = v_H - v_L$ the value range. The welfare decomposition identifies a per-trade transfer $\\mu\\eta\\Delta$ from the protoco"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.19742","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.19742/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}