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| Format: | Preprint |
| Published: |
2026
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| Online Access: | https://arxiv.org/abs/2605.19742 |
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| _version_ | 1866917550106869760 |
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| author | Nakamura, Yuki |
| author_facet | Nakamura, Yuki |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_19742 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Privacy Subsidy in Glosten-Milgrom: Bid-Ask Spread and Welfare under Flip-Noise Direction Observation Nakamura, Yuki Computer Science and Game Theory Cryptography and Security Probability Trading and Market Microstructure 91B26, 91G80, 91G15 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. |
| title | The Privacy Subsidy in Glosten-Milgrom: Bid-Ask Spread and Welfare under Flip-Noise Direction Observation |
| topic | Computer Science and Game Theory Cryptography and Security Probability Trading and Market Microstructure 91B26, 91G80, 91G15 |
| url | https://arxiv.org/abs/2605.19742 |