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Bayesian privacy

Author

Listed:
  • Eilat, Ran

    (Department of Economics, Ben-Gurion University of the Negev)

  • Eliaz, Kfir

    (Department of Economics, Tel-Aviv University and University of Utah)

  • Mu, Xiaosheng

    (Department of Economics, Princeton University)

Abstract

Modern information technologies make it possible to store, analyze and trade unprecedented amounts of detailed information about individuals. This has led to public discussions on whether individuals' privacy should be better protected by restricting the amount or the precision of information that is collected by commercial institutions on their participants. We contribute to this discussion by proposing a Bayesian approach to measure loss of privacy in a mechanism. Specifically, we define the loss of privacy associated with a mechanism as the difference between the designer's prior and posterior beliefs about an agent's type, where this difference is calculated using Kullback-Leibler divergence, and where the change in beliefs is triggered by actions taken by the agent in the mechanism. We consider both ex-post (for every realized type, the maximal difference in beliefs cannot exceed some threshold κ) and ex-ante (the expected difference in beliefs over all type realizations cannot exceed some threshold κ) measures of privacy loss. Applying these notions to the monopolistic screening environment of Mussa and Rosen (1978), we study the properties of optimal privacy-constrained mechanisms and the relation between welfare/profits and privacy levels.

Suggested Citation

  • Eilat, Ran & Eliaz, Kfir & Mu, Xiaosheng, 2021. "Bayesian privacy," Theoretical Economics, Econometric Society, vol. 16(4), November.
    • Handle: RePEc:the:publsh:4390
    as

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    References listed on IDEAS

    as
    1. Choi, Jay Pil & Jeon, Doh-Shin & Kim, Byung-Cheol, 2019. "Privacy and personal data collection with information externalities," Journal of Public Economics, Elsevier, vol. 173(C), pages 113-124.
    2. David Laibson, 2018. "Private Paternalism, the Commitment Puzzle, and Model-Free Equilibrium," AEA Papers and Proceedings, American Economic Association, vol. 108, pages 1-21, May.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. Mackenzie, Andrew & Zhou, Yu, 2022. "Menu mechanisms," Journal of Economic Theory, Elsevier, vol. 204(C).

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    More about this item

    Keywords

    Privacy; mechanism design; relative entropy;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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