The Privacy Subsidy in Continuous-Time Kyle: Cumulative Welfare under Noise-Perturbed Order-Flow Observation
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911735691083776 |
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| author | Nakamura, Yuki |
| author_facet | Nakamura, Yuki |
| contents | 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 correspondence 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 continuous-time Kyle leg of the program of quantifying break-even fees for committed-AMM exchanges under privacy-aggregated information environments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_25631 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Privacy Subsidy in Continuous-Time Kyle: Cumulative Welfare under Noise-Perturbed Order-Flow Observation Nakamura, Yuki Computer Science and Game Theory Cryptography and Security Probability Trading and Market Microstructure 91B26, 91G80, 91G15 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 correspondence 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 continuous-time Kyle leg of the program of quantifying break-even fees for committed-AMM exchanges under privacy-aggregated information environments. |
| title | The Privacy Subsidy in Continuous-Time Kyle: Cumulative Welfare under Noise-Perturbed Order-Flow Observation |
| topic | Computer Science and Game Theory Cryptography and Security Probability Trading and Market Microstructure 91B26, 91G80, 91G15 |
| url | https://arxiv.org/abs/2605.25631 |