The Privacy Subsidy: Kyle's $λ$ under Noise-Perturbed Order-Flow Observation
For designers of privacy-preserving cryptocurrency exchanges, this provides a theoretical foundation for pricing privacy, though the result is limited to a specific noise model and leaves other designs for future work.
The paper derives the unique linear Kyle equilibrium when a market maker observes order flow with Gaussian privacy noise, showing that price impact and informed strategy rescale by a single factor and their product is invariant. It identifies a closed-form 'privacy subsidy'—the break-even fee for privacy-aggregated exchanges—analogous to Loss-Versus-Rebalancing.
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.