The Privacy Subsidy in Glosten-Milgrom: Bid-Ask Spread and Welfare under Flip-Noise Direction Observation

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Field	Value
Primary domain	Unclassified
Other domains	—
Methods	Research Methods
Facets	—
Authors	Yuki Nakamura
Published	2026-05-31
Source	arXiv Quantitative Finance History
Identifiers	arxiv:2605.19742
URL	Open original source

Editorial synthesis

Why it matters

The study adds trade-direction privacy noise to the Glosten–Milgrom sequential-trading model, directly linking privacy mechanisms to bid-ask spreads and welfare transfers. (abstract:S1, abstract:S2, abstract:S3)

Main author claims

• The authors derive a closed-form bid-ask spread and welfare decomposition when the market maker observes trade direction through a binary flip channel. (abstract:S1)
• The authors report: Under a committed Bayesian market-maker rule, the authors give the equilibrium spread as mu(1-2 eta)Delta and identify a per-trade mu eta Delta transfer from the liquidity pool to traders as a “privacy subsidy.” (abstract:S2, abstract:S3)
• The authors claim that the result extends the privacy-subsidy concept from a continuous Gaussian setting to discrete two-state microstructure and identify noisy direction disclosure in MPC matching engines as an application. (abstract:S4, abstract:S5)

Data, method, or discussion scope

The material is a closed-form theoretical analysis within a Glosten–Milgrom model using binary flip noise and committed Bayesian pricing, with a proposed privacy-preserving matching-engine application. (abstract:S1, abstract:S2, abstract:S3, abstract:S4, abstract:S5)

Main limitations

The conclusions depend on a two-state microstructure, binary noise, and committed-pricing assumptions; the MPC matching engine is presented as an application rather than supported by deployment or empirical validation. (abstract:S1, abstract:S2, abstract:S4, abstract:S5)

Relationships

• None recorded.