The Privacy Subsidy: Kyle's $λ$ under Noise-Perturbed Order-Flow Observation

• URL: http://arxiv.org/abs/2605.15746v2
• Date: Tue, 19 May 2026 11:56:40 GMT
• Title: The Privacy Subsidy: Kyle's $λ$ under Noise-Perturbed Order-Flow Observation
• Abstract summary: Privacy-preserving cryptocurrency exchanges alter what the pricing mechanism observes about order flow.<n>We derive the unique linear Kyle equilibrium when a committed Bayesian market maker observes order flow perturbed by independent Gaussian privacy noise.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Privacy-preserving cryptocurrency exchanges (shielded AMMs, batched swap auctions, sealed-bid order-flow auctions) alter what the pricing mechanism observes about order flow. We derive the unique linear Kyle equilibrium when a committed Bayesian market maker observes order flow perturbed by independent Gaussian privacy noise. The price-impact coefficient and informed-trader strategy both rescale by a single factor in the privacy parameter, and their product is invariant. A welfare decomposition then identifies a closed-form per-period transfer from the protocol's LP pool to traders -- the "privacy subsidy", the break-even fee any privacy-aggregated exchange must charge. The result is the single-period closed-form privacy-noise analog of Loss-Versus-Rebalancing (Milionis et al. 2022). The primary application is shielded AMMs with explicit additive-noise injection (e.g., differential privacy); related designs (batched swaps, sealed-bid auctions, oracle-pegged crossings) require separate frameworks that we leave to future work.

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