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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2605.15746 |
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| _version_ | 1866917550086946816 |
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| author | Nakamura, Yuki |
| author_facet | Nakamura, Yuki |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_15746 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Privacy Subsidy: Kyle's $λ$ under Noise-Perturbed Order-Flow Observation Nakamura, Yuki Computer Science and Game Theory Cryptography and Security Probability Trading and Market Microstructure 91B26, 91G80, 91G15 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. |
| title | The Privacy Subsidy: Kyle's $λ$ 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/2605.15746 |