Privacy costs quantified: New paper shows traders get a 'privacy subsidy' in markets

Yuki Nakamura's latest paper, 'The Privacy Subsidy in Glosten-Milgrom: Bid-Ask Spread and Welfare under Flip-Noise Direction Observation,' provides a rigorous mathematical foundation for the cost of privacy in financial markets. The author extends the classic 1985 Glosten-Milgrom sequential-trading model to incorporate a binary flip channel of probability η on the trade direction observed by the market maker. Under a committed Bayesian pricing rule, the equilibrium bid-ask spread simplifies to μ(1-2η)Δ, where μ is the informed-trader fraction and Δ the value range. Crucially, Nakamura identifies a 'privacy subsidy'—a per-trade transfer of μηΔ from the protocol's liquidity pool to traders. This mirrors a similar finding in the continuous Gaussian Kyle model, proving the concept's robustness across the two canonical market microstructure frameworks.

The results have immediate practical implications. The primary application is in MPC-based (multi-party computation) matching engines with ε-differentially-private direction disclosure: when the engine prices on a noisy signal, the subsidy reduces the effective spread by exactly the amount of noise injected. This means privacy-protecting mechanisms don't simply add cost; they redistribute welfare from liquidity providers to traders, potentially narrowing effective spreads. The paper is a companion to Nakamura's earlier work (arXiv:2605.15746) on the Gaussian case and runs only 9 pages, offering a clean theoretical result for crypto engineers, market designers, and anyone building privacy-preserving trading infrastructure. It also bridges cryptographya (CS.CR) and financial economics (q-fin.TR), making it a must-read for cross-disciplinary audiences.