Pith Number

pith:AXFQH7SQ

pith:2026:AXFQH7SQOOPLAQ73RTHIBRQGBT

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

Yuki Nakamura

In a Kyle model with Gaussian privacy noise added to order flow, the price-impact coefficient and informed-trader strategy rescale by the same factor so their product stays fixed and a closed-form per-period transfer arises from the LP pool

arxiv:2605.15746 v1 · 2026-05-15 · cs.GT · cs.CR · math.PR · q-fin.TR

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Claims

C1strongest claim

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.

C2weakest assumption

The market maker is a committed Bayesian observer of order flow that has been perturbed by independent Gaussian privacy noise, and that a unique linear equilibrium exists under this observation model.

C3one line summary

Derives closed-form rescaling of Kyle lambda and informed strategy under Gaussian order-flow noise, with invariant product and explicit privacy subsidy from liquidity providers to traders.

References

17 extracted · 17 resolved · 0 Pith anchors

[1] arXiv preprint arXiv:1908.08777 (2019) 1908

[2] https: //whitepaper.renegade.fi/(2024), accessed 2026-05-15 2024

[3] Journal of Economic Literature57(1), 44–95 (2019) 2019

[4] arXiv preprint arXiv:2501.16488 (2025) 2025

[5] In: Proceedings of the ACM Conference on Electronic Commerce (2012) 2012

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:01:16.001758Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

05cb03fe50739eb043fb8cce80c6060ce33cf8d10a94652450bbde087ac5bd5d

Aliases

arxiv: 2605.15746 · arxiv_version: 2605.15746v1 · doi: 10.48550/arxiv.2605.15746 · pith_short_12: AXFQH7SQOOPL · pith_short_16: AXFQH7SQOOPLAQ73 · pith_short_8: AXFQH7SQ

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/AXFQH7SQOOPLAQ73RTHIBRQGBT \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 05cb03fe50739eb043fb8cce80c6060ce33cf8d10a94652450bbde087ac5bd5d

Canonical record JSON

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      "math.PR",
      "q-fin.TR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.GT",
    "submitted_at": "2026-05-15T08:56:16Z",
    "title_canon_sha256": "cb659ae9f23692c7d834066c0a64b2a6bd513633dcb79938bcf6ed265de7d80b"
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