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 $\sigma_\varepsilon$. Under the Markovian linear equilibrium, the price-impact coefficient is $\lambda = \sigma_v / \sqrt{\sigma_u^2 + \sigma_\varepsilon^2}$ -- constant in time -- and the cumulative expected transfer from the protocol's liquidity pool to traders over $[0,1]$ is $|\Pi_M| = \sigma_v \sigma_\varepsilon^2 / \sqrt{\sigma_u^2 + \sigma_\varepsilon^2}$. 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.
| Comments: | 13 pages. Third paper in a privacy-subsidy cluster (companions: arXiv:2605.15746, arXiv:2605.19742). Continuous-time Kyle analog with closed-form cumulative subsidy and structural duality to LVR (Milionis et al. 2022) |
| Subjects: | Computer Science and Game Theory (cs.GT); Cryptography and Security (cs.CR); Probability (math.PR); Trading and Market Microstructure (q-fin.TR) |
| MSC classes: | 91B26, 91G80, 91G15 |
| Cite as: | arXiv:2605.25631 [cs.GT] |
| (or arXiv:2605.25631v1 [cs.GT] for this version) | |
| https://doi.org/10.48550/arXiv.2605.25631 arXiv-issued DOI via DataCite (pending registration) |
From: Yuki Nakamura [view email]
[v1]
Mon, 25 May 2026 09:31:40 UTC (14 KB)
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