Privacy Noise, Price Impact, and Trader Transfers in Kyle Markets

Summary

This document analyzes how privacy noise affects price formation in a Kyle-style market. It assumes a committed Bayesian market maker observes order flow mixed with independent Gaussian noise, then derives a unique linear equilibrium. In that equilibrium, the market maker’s price-impact coefficient and the informed trader’s strategy change in reciprocal directions as the privacy parameter changes, leaving their product unchanged.

A welfare decomposition yields a closed-form transfer from the protocol’s liquidity-provider pool to traders, termed a privacy subsidy. The authors interpret this transfer as the break-even fee for an exchange using privacy-aggregated order flow, and relate the result to a single-period analogue of Loss-Versus-Rebalancing. The stated application is shielded automated market makers that add noise, including differential privacy designs. The analysis is theoretical and single-period; batched swaps, sealed-bid auctions, and oracle-pegged crossings are explicitly outside its framework and require separate analysis.

Key ideas

• The model studies a market maker pricing order flow perturbed by independent Gaussian privacy noise.
• Privacy changes price impact and informed trading in reciprocal ways while their product stays invariant.
• A welfare decomposition identifies a transfer from the liquidity-provider pool to traders.
• The resulting subsidy gives a break-even fee for the modeled privacy-aggregated exchange.
• The framework is single-period and does not cover several other privacy-preserving market designs.

Tags

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


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









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.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.