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 $η$ -- 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 $μ(1-2η)Δ$, where $μ$ is the informed-trader fraction and $Δ= v_H - v_L$ the value range. The welfare decomposition identifies a per-trade transfer $μηΔ$ from the protocol's liquidity pool to traders -- the "privacy subsidy", mirroring the Gaussian-Kyle analog established in prior work. The result extends the privacy-subsidy concept from continuous Gaussian to discrete two-state microstructure, demonstrating robustness across both classical models. Primary application: MPC-based matching engines with $\varepsilon$-differentially-private direction disclosure, where the engine prices on a noisy direction signal.

翻译：我们推导了当做市商通过概率为$η$的二元翻转信道观测到受扰动的交易方向时——即隐私机制作用于方向信号的自然信息论模型——格罗斯滕-米尔格罗姆1985序贯交易模型中的封闭形式买卖价差与福利分解。在贝叶斯做市商承诺定价规则下，均衡价差为$μ(1-2η)Δ$，其中$μ$为知情交易者比例，$Δ= v_H - v_L$为资产价值区间。福利分解识别出从协议流动性池向交易者的每笔交易转移$μηΔ$——即"隐私补贴"，这与先前工作中建立的高斯-凯尔模型类似。该结果将隐私补贴概念从连续高斯微观结构拓展至离散两状态微观结构，展示了该概念在两个经典模型中的稳健性。主要应用场景：基于安全多方计算（MPC）的撮合引擎采用$\varepsilon$差分隐私方向披露机制，该引擎依据带噪方向信号进行定价。