[go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2112.14356.html
   My bibliography  Save this paper

Private Private Information

Author

Listed:
  • Kevin He
  • Fedor Sandomirskiy
  • Omer Tamuz
Abstract
Private signals model noisy information about an unknown state. Although these signals are called "private," they may still carry information about each other. Our paper introduces the concept of private private signals, which contain information about the state but not about other signals. To achieve privacy, signal quality may need to be sacrificed. We study the informativeness of private private signals and characterize those that are optimal in the sense that they cannot be made more informative without violating privacy. We discuss implications for privacy in recommendation systems, information design, causal inference, and mechanism design.

Suggested Citation

  • Kevin He & Fedor Sandomirskiy & Omer Tamuz, 2021. "Private Private Information," Papers 2112.14356, arXiv.org, revised Sep 2024.
    • Handle: RePEc:arx:papers:2112.14356
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2112.14356
    File Function: Latest version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Bergemann, Dirk & Morris, Stephen, 2016. "Bayes correlated equilibrium and the comparison of information structures in games," Theoretical Economics, Econometric Society, vol. 11(2), May.
    2. Alexey Kushnir, 2013. "On the equivalence between Bayesian and dominant strategy implementation: the case of correlated types," ECON - Working Papers 129, Department of Economics - University of Zurich.
    3. Hong, Lu & Page, Scott, 2009. "Interpreted and generated signals," Journal of Economic Theory, Elsevier, vol. 144(5), pages 2174-2196, September.
    4. Dirk Bergemann & Benjamin Brooks & Stephen Morris, 2017. "First‐Price Auctions With General Information Structures: Implications for Bidding and Revenue," Econometrica, Econometric Society, vol. 85, pages 107-143, January.
    5. Ina Taneva, 2019. "Information Design," American Economic Journal: Microeconomics, American Economic Association, vol. 11(4), pages 151-185, November.
    6. Filip Matêjka & Alisdair McKay, 2015. "Rational Inattention to Discrete Choices: A New Foundation for the Multinomial Logit Model," American Economic Review, American Economic Association, vol. 105(1), pages 272-298, January.
    7. Laurent Mathevet & Jacopo Perego & Ina Taneva, 2020. "On Information Design in Games," Journal of Political Economy, University of Chicago Press, vol. 128(4), pages 1370-1404.
    8. A. Dawid & M. DeGroot & J. Mortera & R. Cooke & S. French & C. Genest & M. Schervish & D. Lindley & K. McConway & R. Winkler, 1995. "Coherent combination of experts' opinions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 4(2), pages 263-313, December.
    9. Itai Arieli & Yakov Babichenko & Fedor Sandomirskiy & Omer Tamuz, 2021. "Feasible Joint Posterior Beliefs," Journal of Political Economy, University of Chicago Press, vol. 129(9), pages 2546-2594.
    10. Michael Ostrovsky, 2012. "Information Aggregation in Dynamic Markets With Strategic Traders," Econometrica, Econometric Society, vol. 80(6), pages 2595-2647, November.
    11. Elchanan Mossel & Manuel Mueller‐Frank & Allan Sly & Omer Tamuz, 2020. "Social Learning Equilibria," Econometrica, Econometric Society, vol. 88(3), pages 1235-1267, May.
    12. Gale, Douglas, 1996. "What have we learned from social learning?," European Economic Review, Elsevier, vol. 40(3-5), pages 617-628, April.
    13. repec:dau:papers:123456789/387 is not listed on IDEAS
    14. Alex Gershkov & Jacob K. Goeree & Alexey Kushnir & Benny Moldovanu & Xianwen Shi, 2013. "On the Equivalence of Bayesian and Dominant Strategy Implementation," Econometrica, Econometric Society, vol. 81(1), pages 197-220, January.
    15. Viossat, Yannick, 2008. "Is having a unique equilibrium robust?," Journal of Mathematical Economics, Elsevier, vol. 44(11), pages 1152-1160, December.
    16. Sims, Christopher A., 2010. "Rational Inattention and Monetary Economics," Handbook of Monetary Economics, in: Benjamin M. Friedman & Michael Woodford (ed.), Handbook of Monetary Economics, edition 1, volume 3, chapter 4, pages 155-181, Elsevier.
    17. Benjamin Brooks & Songzi Du, 2021. "Optimal Auction Design With Common Values: An Informationally Robust Approach," Econometrica, Econometric Society, vol. 89(3), pages 1313-1360, May.
    18. Itai Arieli & Yakov Babichenko & Fedor Sandomirskiy & Omer Tamuz, 2020. "Feasible Joint Posterior Beliefs," Papers 2002.11362, arXiv.org, revised Dec 2020.
    19. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, December.
    20. Forges, Francoise, 1990. "Correlated Equilibrium in Two-Person Zero-Sum Games," Econometrica, Econometric Society, vol. 58(2), pages 515-515, March.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Xu Lang, 2023. "A Belief-Based Characterization of Reduced-Form Auctions," Papers 2307.04070, arXiv.org.
    2. Tommaso Denti & Doron Ravid, 2023. "Robust Predictions in Games with Rational Inattention," Papers 2306.09964, arXiv.org.
    3. Takashi Ui, 2020. "LQG Information Design," Working Papers on Central Bank Communication 018, University of Tokyo, Graduate School of Economics.
    4. P. Jean-Jacques Herings & Dominik Karos & Toygar T. Kerman, 2024. "Belief inducibility and informativeness," Theory and Decision, Springer, vol. 96(4), pages 517-553, June.
    5. Chan, Jimmy & Gupta, Seher & Li, Fei & Wang, Yun, 2019. "Pivotal persuasion," Journal of Economic Theory, Elsevier, vol. 180(C), pages 178-202.
      • Jimmy Chan & Seher Gupta & Fei Li & Yun Wang, 2018. "Pivotal Persuasion," Working Papers 2018-11-03, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    6. Itai Arieli & Yakov Babichenko & Fedor Sandomirskiy, 2023. "Feasible Conditional Belief Distributions," Papers 2307.07672, arXiv.org, revised Nov 2024.
    7. Deniz Kattwinkel & Axel Niemeyer & Justus Preusser & Alexander Winter, 2023. "Mechanisms without transfers for fully biased agents," CRC TR 224 Discussion Paper Series crctr224_2023_485, University of Bonn and University of Mannheim, Germany.
    8. Dirk Bergemann & Stephen Morris, 2016. "Information Design, Bayesian Persuasion, and Bayes Correlated Equilibrium," American Economic Review, American Economic Association, vol. 106(5), pages 586-591, May.
    9. Carl Heese & Stephan Lauermann, 2021. "Persuasion and Information Aggregation in Elections," ECONtribute Discussion Papers Series 112, University of Bonn and University of Cologne, Germany.
    10. Deniz Kattwinkel & Axel Niemeyer & Justus Preusser & Alexander Winter, 2022. "Mechanisms without transfers for fully biased agents," Papers 2205.10910, arXiv.org.
    11. Masaki Miyashita & Takashi Ui, 2023. "LQG Information Design," Papers 2312.09479, arXiv.org, revised Jun 2024.
    12. Feng, Xin, 2020. "Information disclosure on the contest mechanism," Journal of Mathematical Economics, Elsevier, vol. 91(C), pages 148-156.
    13. Itai Arieli & Yakov Babichenko & Fedor Sandomirskiy & Omer Tamuz, 2020. "Feasible Joint Posterior Beliefs," Papers 2002.11362, arXiv.org, revised Dec 2020.
    14. Tomala, Tristan & Koessler, Frederic & Laclau, Marie, 2018. "Interactive Information Design," HEC Research Papers Series 1260, HEC Paris, revised 02 May 2018.
    15. Koessler, Frédéric & Skreta, Vasiliki, 2016. "Informed seller with taste heterogeneity," Journal of Economic Theory, Elsevier, vol. 165(C), pages 456-471.
    16. Li, Fei & Song, Yangbo & Zhao, Mofei, 2023. "Global manipulation by local obfuscation," Journal of Economic Theory, Elsevier, vol. 207(C).
    17. Dirk Bergemann & Stephen Morris, 2019. "Information Design: A Unified Perspective," Journal of Economic Literature, American Economic Association, vol. 57(1), pages 44-95, March.
    18. Goeree, Jacob K. & Kushnir, Alexey, 2016. "Reduced form implementation for environments with value interdependencies," Games and Economic Behavior, Elsevier, vol. 99(C), pages 250-256.
    19. Oriol Carbonell-Nicolau, 2021. "Equilibria in infinite games of incomplete information," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(2), pages 311-360, June.
    20. Larionov, Daniil & Pham, Hien & Yamashita, Takuro & Zhu, Shuguang, 2021. "First Best Implementation with Costly Information Acquisition," TSE Working Papers 21-1261, Toulouse School of Economics (TSE), revised Apr 2022.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2112.14356. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.