New paper quantifies the true cost of privacy in DeFi exchanges

In a new paper posted to arXiv, researcher Yuki Nakamura tackles a fundamental question for privacy-preserving decentralized exchanges: what is the exact cost of hiding order flow? The work, titled The Privacy Subsidy: Kyle's λ under Noise-Perturbed Order-Flow Observation, applies Kyle's classic model of strategic insider trading to a market where the market maker only sees a noise-perturbed version of aggregate order flow—modeled as the true order flow plus independent Gaussian privacy noise. Nakamura solves for the unique linear equilibrium, showing that both the price-impact coefficient (λ) and the informed trader's aggressiveness rescale by the same factor determined by the privacy parameter. Crucially, their product remains invariant, mirroring a key property of the original Kyle model.

The central result is a closed-form expression for a per-period transfer from the exchange's liquidity pool to traders—the 'privacy subsidy.' This subsidy represents the minimum fee any privacy-aggregated exchange (like a shielded automated market maker) must charge to break even relative to a fully transparent market. Nakamura explicitly connects this to Loss-Versus-Rebalancing (Milionis et al., 2022), establishing the privacy-noise analog of that important DeFi metric. The paper focuses on additive-noise injection (e.g., differential privacy) and leaves batched swaps, sealed-bid auctions, and oracle-pegged crossings to future work. For DeFi designers, this provides a rigorous framework to evaluate the economic trade-offs between privacy and liquidity provider compensation.