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Privacy‐Preserving Signals

Author

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  • Philipp Strack
  • Kai Hao Yang

Abstract

A signal is privacy‐preserving with respect to a collection of privacy sets if the posterior probability assigned to every privacy set remains unchanged conditional on any signal realization. We characterize the privacy‐preserving signals for arbitrary state space and arbitrary privacy sets. A signal is privacy‐preserving if and only if it is a garbling of a reordered quantile signal. Furthermore, distributions of posterior means induced by privacy‐preserving signals are exactly mean‐preserving contractions of that induced by the quantile signal. We discuss the economic implications of our characterization for statistical discrimination, the revelation of sensitive information in auctions and price discrimination.

Suggested Citation

  • Philipp Strack & Kai Hao Yang, 2024. "Privacy‐Preserving Signals," Econometrica, Econometric Society, vol. 92(6), pages 1907-1938, November.
    • Handle: RePEc:wly:emetrp:v:92:y:2024:i:6:p:1907-1938
    DOI: 10.3982/ECTA22017
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    References listed on IDEAS

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    1. Andreas Kleiner & Benny Moldovanu & Philipp Strack, 2021. "Extreme Points and Majorization: Economic Applications," Econometrica, Econometric Society, vol. 89(4), pages 1557-1593, July.
    2. Shota Ichihashi, 2020. "Online Privacy and Information Disclosure by Consumers," American Economic Review, American Economic Association, vol. 110(2), pages 569-595, February.
    3. Laura Doval & Alex Smolin, 2024. "Persuasion and Welfare," Journal of Political Economy, University of Chicago Press, vol. 132(7), pages 2451-2487.
    4. Kolotilin, Anton, 2018. "Optimal information disclosure: a linear programming approach," Theoretical Economics, Econometric Society, vol. 13(2), May.
    5. S Nageeb Ali & Nima Haghpanah & Xiao Lin & Ron Siegel, 2022. "How to Sell Hard Information," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 137(1), pages 619-678.
    6. FORGES , Françoise, 1993. "Five Legitimate Definitions of Correlated Equilibrium in Games with Incomplete Information," LIDAM Discussion Papers CORE 1993009, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    7. Jerry R. Green & Nancy L. Stokey, 2022. "Two representations of information structures and their comparisons," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 45(2), pages 541-547, December.
    8. Dirk Bergemann & Tibor Heumann & Stephen Morris, 2023. "Bidder-Optimal Information Structures in Auctions," Cowles Foundation Discussion Papers 2375, Cowles Foundation for Research in Economics, Yale University.
    9. Talia Gillis & Bryce McLaughlin & Jann Spiess, 2021. "On the Fairness of Machine-Assisted Human Decisions," Papers 2110.15310, arXiv.org, revised Sep 2023.
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    Citations

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    Cited by:

    1. Costas Cavounidis & Massimiliano Furlan & Alkis Georgiadis-Harris, 2025. "Perfect Secrecy in the Wild: A Characterization," Papers 2506.12416, arXiv.org.
    2. Tommaso Bondi & Omid Rafieian & Yunfei (Jesse) Yao, 2026. "Privacy and Polarization: An Inference-Based Framework," Management Science, INFORMS, vol. 72(2), pages 1389-1409, February.
    3. Zhang Xu & Wei Zhao, 2025. "Privacy-Constrained Signals," Papers 2511.21196, arXiv.org.
    4. Zhang Xu & Wei Zhao, 2025. "Privacy Structure and Blackwell Frontier," Papers 2511.10226, arXiv.org.

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