The Privacy Subsidy in Continuous-Time Kyle: Cumulative Welfare under Noise-Perturbed Order-Flow Observation
2026-05-25 • Computer Science and Game Theory
Computer Science and Game TheoryCryptography and Security
AI summaryⓘ
The authors extend previous work on how privacy affects trading in financial markets from a single time period to a continuous timeline. They study a market maker who sees trade information mixed with random noise to protect privacy, and find a formula for how this noise influences trading costs and prices over time. They also connect this privacy effect to a concept called Loss-Versus-Rebalancing, showing a deep relationship between how privacy noise and price observation gaps impact market welfare. Their work helps to understand the fees and subsidies needed in markets that use privacy to aggregate trade information.
Kyle modelautomated market makerprivacy noiseBrownian motionprice-impact coefficientBayesian equilibriumLoss-Versus-Rebalancingwelfare analysiscontinuous-time financeprivacy subsidy
Authors
Yuki Nakamura
Abstract
We extend the closed-form privacy-subsidy result of Nakamura~(2026, arXiv:2605.15746) from the single-period Kyle model to continuous-time. A committed Bayesian automated market maker observes the aggregate order flow perturbed by an independent Brownian privacy channel of diffusion intensity $σ_\varepsilon$. Under the Markovian linear equilibrium, the price-impact coefficient is $λ= σ_v / \sqrt{σ_u^2 + σ_\varepsilon^2}$ -- constant in time -- and the cumulative expected transfer from the protocol's liquidity pool to traders over $[0,1]$ is $|Π_M| = σ_v σ_\varepsilon^2 / \sqrt{σ_u^2 + σ_\varepsilon^2}$. We then establish a structural duality between this cumulative privacy subsidy and Loss-Versus-Rebalancing (Milionis et al.~2022), identifying privacy-noise welfare as the order-flow observation analog of LVR's price observation gap. The result completes the program of quantifying break-even fees for committed-AMM exchanges under privacy-aggregated information environments.