Yuki Nakamura extends privacy-subsidy model to continuous-time Kyle AMMs

Yuki Nakamura has released a new paper that extends the closed-form privacy-subsidy result from a single-period Kyle model to a continuous-time setting. The work models a committed Bayesian automated market maker (AMM) that observes aggregate order flow perturbed by an independent Brownian privacy channel of diffusion intensity σ_ε. In the Markovian linear equilibrium, the price-impact coefficient λ becomes constant over time, expressed as λ = σ_v / √(σ_u² + σ_ε²). This leads to a closed-form cumulative expected transfer from the protocol's liquidity pool to traders over the interval [0,1]: |Π_M| = σ_v σ_ε² / √(σ_u² + σ_ε²).

Crucially, the paper establishes a structural duality between this cumulative privacy subsidy and the Loss-Versus-Rebalancing (LVR) measure introduced by Milionis et al. (2022). Nakamura identifies privacy-noise welfare as the order-flow observation analog of LVR's price-observation gap. The result completes a program to quantify break-even fees for committed-AMM exchanges operating under privacy-aggregated information environments. The paper is the third in a cluster of works by Nakamura (companions: arXiv:2605.15746, arXiv:2605.19742) and runs 13 pages, contributing to computer science and game theory, cryptography, probability, and trading microstructure.