The Privacy Subsidy: Kyle's $\lambda$ under Noise-Perturbed Order-Flow Observation

Computer Science > Computer Science and Game Theory [Submitted on 15 May 2026] The Privacy Subsidy: Kyle's λ under Noise-Perturbed Order-Flow Observation Yuki Nakamura Privacy-preserving cryptocurrency exchanges (shielded AMMs, batched swap auctions, sealed-bid order-flow auctions) 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 both rescale by a single factor in the privacy parameter, and 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. Comments: 16 pages, 1 figure 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:2605.15746 [cs.GT]   (or arXiv:2605.15746v1 [cs.GT] for this version)   https://doi.org/10.48550/arXiv.2605.15746 Focus to learn more Submission history From: Yuki Nakamura [view email] [v1] Fri, 15 May 2026 08:56:16 UTC (15 KB) Access Paper: HTML (experimental) view license Current browse context: cs.GT < prev   |   next > new | recent | 2026-05 Change to browse by: cs cs.CR math math.PR q-fin q-fin.TR References & Citations NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)