IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2410.21694.html

Weighted Garbling

Author

Listed:
  • Daehyun Kim
  • Ichiro Obara

Abstract

We introduce an information order on experiments based on weighted garbling, a generalization of the standard notion of garbling. In this order, an experiment is more informative than another if the latter is a weighted garbling of the former. We show that this is equivalent to ordinary garbling conditional on a payoff-irrelevant event. We also characterize the order in terms of induced posterior belief distributions, showing that it depends only on their support. Our main results provide two decision-theoretic characterizations of this order. First, in static decision problems, one experiment dominates another if and only if its value of information is at least a fixed fraction of the other's across all problems. Second, in a class of stopping time problems with a hidden Markov process and repeated experimentation, one experiment dominates another if and only if it yields weakly higher expected payoffs for every problem with a regular prior.

Suggested Citation

  • Daehyun Kim & Ichiro Obara, 2024. "Weighted Garbling," Papers 2410.21694, arXiv.org, revised Mar 2026.
    • Handle: RePEc:arx:papers:2410.21694
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2410.21694
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Yaron Azrieli, 2014. "Comment on “The Law of Large Demand for Information”," Econometrica, Econometric Society, vol. 82(1), pages 415-423, January.
    2. Antonio Cabrales & Olivier Gossner & Roberto Serrano, 2013. "Entropy and the Value of Information for Investors," American Economic Review, American Economic Association, vol. 103(1), pages 360-377, February.
    3. Giuseppe Moscarini & Lones Smith, 2002. "The Law of Large Demand for Information," Econometrica, Econometric Society, vol. 70(6), pages 2351-2366, November.
    4. Christopher Phelan & Andrzej Skrzypacz, 2012. "Beliefs and Private Monitoring," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 79(4), pages 1637-1660.
    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. Xiaosheng Mu & Luciano Pomatto & Philipp Strack & Omer Tamuz, 2021. "From Blackwell Dominance in Large Samples to Rényi Divergences and Back Again," Econometrica, Econometric Society, vol. 89(1), pages 475-506, January.
    2. Cabrales, Antonio & Gossner, Olivier & Serrano, Roberto, 2017. "A normalized value for information purchases," Journal of Economic Theory, Elsevier, vol. 170(C), pages 266-288.
    3. Ehud Lehrer & Tao Wang, 2024. "The value of information in stopping problems," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 78(2), pages 619-648, September.
    4. Athey, Susan & Levin, Jonathan, 2018. "The value of information in monotone decision problems," Research in Economics, Elsevier, vol. 72(1), pages 101-116.
    5. Ehud Lehrer & Tao Wang, 2022. "The Value of Information in Stopping Problems," Papers 2205.06583, arXiv.org.
    6. Mira Frick & Ryota Iijima & Yuhta Ishii, 2021. "Learning Efficiency of Multi-Agent Information Structures," Cowles Foundation Discussion Papers 2299, Cowles Foundation for Research in Economics, Yale University.
    7. Lindbeck, Assar & Weibull, Jörgen, 2020. "Delegation of investment decisions, and optimal remuneration of agents," European Economic Review, Elsevier, vol. 129(C).
    8. Antonio Cabrales & Olivier Gossner & Roberto Serrano, 2012. "The Appeal of Information Transactions," Working Papers 2012-13, Brown University, Department of Economics.
    9. Akisik, Orhan & Gal, Graham, 2023. "IFRS, financial development and income inequality: An empirical study using mediation analysis," Economic Systems, Elsevier, vol. 47(2).
    10. Kailin Chen, 2025. "Communication with Multiple Senders," Papers 2505.14639, arXiv.org, revised Oct 2025.
    11. Antonio Jiménez-Martínez, 2015. "A model of belief influence in large social networks," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 59(1), pages 21-59, May.
    12. Azevedo, Eduardo M. & Mao, David & Montiel Olea, José Luis & Velez, Amilcar, 2023. "The A/B testing problem with Gaussian priors," Journal of Economic Theory, Elsevier, vol. 210(C).
    13. Phelan, Christopher & Skrzypacz, Andrzej, 2015. "Recall and private monitoring," Games and Economic Behavior, Elsevier, vol. 90(C), pages 162-170.
    14. Agostino Manduchi, 2013. "Non-neutral information costs with match-value uncertainty," Journal of Economics, Springer, vol. 109(1), pages 1-25, May.
    15. Mira Frick & Ryota Iijima & Yuhta Ishii, 2021. "Welfare Comparisons for Biased Learning," Cowles Foundation Discussion Papers 2274, Cowles Foundation for Research in Economics, Yale University.
    16. Henrique de Oliveira & Yuhta Ishii & Xiao Lin, 2021. "Robust Aggregation of Correlated Information," Papers 2106.00088, arXiv.org, revised Sep 2024.
    17. Annie Liang & Xiaosheng Mu & Vasilis Syrgkanis, 2017. "Dynamic Information Acquisition from Multiple Sources," PIER Working Paper Archive 17-023, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 17 Aug 2017.
    18. Zongxia Liang & Qi Ye, 2024. "Optimal information acquisition for eliminating estimation risk," Papers 2405.09339, arXiv.org.
    19. Mensch, Jeffrey, 2021. "Rational inattention and the monotone likelihood ratio property," Journal of Economic Theory, Elsevier, vol. 196(C).
    20. Gonzalo Cisternas & Aaron Kolb, 2020. "Signaling with Private Monitoring," Papers 2007.15514, arXiv.org.

    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:2410.21694. 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.