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

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  • Yuki Nakamura

Abstract

Privacy-preserving cryptocurrency exchanges 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 rescale by reciprocal factors of the privacy parameter (one down, one up), so 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.

Suggested Citation

  • Yuki Nakamura, 2026. "The Privacy Subsidy: Kyle's $\lambda$ under Noise-Perturbed Order-Flow Observation," Papers 2605.15746, arXiv.org, revised May 2026.
    • Handle: RePEc:arx:papers:2605.15746
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    References listed on IDEAS

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