IDEAS home Printed from https://ideas.repec.org/a/eee/mateco/v97y2021ics0304406821001075.html

Bayesian learning with variable prior

Author

Listed:
  • Brandt, Nikolai M.
  • Eckwert, Bernhard
  • Várdy, Felix

Abstract

How much can be learned from a noisy signal about the state of the world not only depends on the accuracy of the signal, but also on the distribution of the prior. Therefore, we define a general information system as a tuple consisting of both a signal technology and a prior. In this paper we develop a learning order for general information systems and characterize the order in two different ways: first, in terms of the dispersion of posterior beliefs about state quantiles and, second, in terms of the value of learning for two different classes of decision makers. The first class includes all agents with quasi-linear quantile preferences, and the second class contains all agents with supermodular quantile preferences.

Suggested Citation

  • Brandt, Nikolai M. & Eckwert, Bernhard & Várdy, Felix, 2021. "Bayesian learning with variable prior," Journal of Mathematical Economics, Elsevier, vol. 97(C).
    • Handle: RePEc:eee:mateco:v:97:y:2021:i:c:s0304406821001075
    DOI: 10.1016/j.jmateco.2021.102544
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304406821001075
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmateco.2021.102544?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Paul Milgrom & Ilya Segal, 2002. "Envelope Theorems for Arbitrary Choice Sets," Econometrica, Econometric Society, vol. 70(2), pages 583-601, March.
    2. Giacomo Corneo & Olivier Jeanne, 2001. "Status, the Distribution of Wealth, and Growth," Scandinavian Journal of Economics, Wiley Blackwell, vol. 103(2), pages 283-293, June.
    3. Nicola Persico, 2000. "Information Acquisition in Auctions," Econometrica, Econometric Society, vol. 68(1), pages 135-148, January.
    4. Diamond, Peter A. & Stiglitz, Joseph E., 1974. "Increases in risk and in risk aversion," Journal of Economic Theory, Elsevier, vol. 8(3), pages 337-360, July.
    5. Bernhard Eckwert & Itzhak Zilcha, 2008. "Efficiency of Screening and Labor Income Inequality," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 10(1), pages 77-98, February.
    6. Brandt, Nikolai & Drees, Burkhard & Eckwert, Bernhard & Várdy, Felix, 2014. "Information and the dispersion of posterior expectations," Journal of Economic Theory, Elsevier, vol. 154(C), pages 604-611.
    7. Robson, Arthur J, 1992. "Status, the Distribution of Wealth, Private and Social Attitudes to Risk," Econometrica, Econometric Society, vol. 60(4), pages 837-857, July.
    8. repec:bla:scandj:v:103:y:2001:i:2:p:283-93 is not listed on IDEAS
    9. Cossette, Hélène & Côté, Marie-Pier & Marceau, Etienne & Moutanabbir, Khouzeima, 2013. "Multivariate distribution defined with Farlie–Gumbel–Morgenstern copula and mixed Erlang marginals: Aggregation and capital allocation," Insurance: Mathematics and Economics, Elsevier, vol. 52(3), pages 560-572.
    10. Bernhard Eckwert & Itzhak Zilcha, 2020. "The role of colleges within the higher education sector," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 69(2), pages 315-336, March.
    11. Justin P. Johnson & David P. Myatt, 2006. "On the Simple Economics of Advertising, Marketing, and Product Design," American Economic Review, American Economic Association, vol. 96(3), pages 756-784, June.
    12. Gould, John P., 1974. "Risk, stochastic preference, and the value of information," Journal of Economic Theory, Elsevier, vol. 8(1), pages 64-84, May.
    13. Feldman, Mark & Gilles, Christian, 1985. "An expository note on individual risk without aggregate uncertainty," Journal of Economic Theory, Elsevier, vol. 35(1), pages 26-32, February.
    14. Athey, Susan & Levin, Jonathan, 2018. "The value of information in monotone decision problems," Research in Economics, Elsevier, vol. 72(1), pages 101-116.
    15. Giuseppe Moscarini & Lones Smith, 2002. "The Law of Large Demand for Information," Econometrica, Econometric Society, vol. 70(6), pages 2351-2366, November.
    16. Juan-JosÈ Ganuza & JosÈ S. Penalva, 2010. "Signal Orderings Based on Dispersion and the Supply of Private Information in Auctions," Econometrica, Econometric Society, vol. 78(3), pages 1007-1030, May.
    17. Paul R. Milgrom, 1981. "Good News and Bad News: Representation Theorems and Applications," Bell Journal of Economics, The RAND Corporation, vol. 12(2), pages 380-391, Autumn.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Kaya, Ayça & Vereshchagina, Galina, 2022. "Sorting expertise," Journal of Economic Theory, Elsevier, vol. 204(C).

    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. Marschak, Thomas & Shanthikumar, J. George & Zhou, Junjie, 2017. "Does more information-gathering effort raise or lower the average quantity produced?," Journal of Mathematical Economics, Elsevier, vol. 69(C), pages 104-117.
    2. Brandt, Nikolai & Drees, Burkhard & Eckwert, Bernhard & Várdy, Felix, 2014. "Information and the dispersion of posterior expectations," Journal of Economic Theory, Elsevier, vol. 154(C), pages 604-611.
    3. Shi, Xianwen, 2012. "Optimal auctions with information acquisition," Games and Economic Behavior, Elsevier, vol. 74(2), pages 666-686.
    4. Yunan Li, 2017. "Efficient Mechanisms with Information Acquisition," PIER Working Paper Archive 16-007, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 23 Jun 2017.
    5. Szalay, Dezsö, 2009. "Contracts with endogenous information," Games and Economic Behavior, Elsevier, vol. 65(2), pages 586-625, March.
    6. Athey, Susan & Levin, Jonathan, 2018. "The value of information in monotone decision problems," Research in Economics, Elsevier, vol. 72(1), pages 101-116.
    7. Cabrales, Antonio & Gossner, Olivier & Serrano, Roberto, 2017. "A normalized value for information purchases," Journal of Economic Theory, Elsevier, vol. 170(C), pages 266-288.
    8. Antonio Cabrales & Olivier Gossner & Roberto Serrano, 2012. "The Appeal of Information Transactions," Working Papers 2012-13, Brown University, Department of Economics.
    9. Mira Frick & Ryota Iijima & Yuhta Ishii, 2021. "Learning Efficiency of Multi-Agent Information Structures," Cowles Foundation Discussion Papers 2299R, Cowles Foundation for Research in Economics, Yale University, revised Dec 2021.
    10. Li, Yunan, 2019. "Efficient mechanisms with information acquisition," Journal of Economic Theory, Elsevier, vol. 182(C), pages 279-328.
    11. Florian Hoffmann & Roman Inderst & Marco Ottaviani, 2013. "Hypertargeting, Limited Attention, and Privacy: Implications for Marketing and Campaigning," Working Papers 479, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    12. Maxim Ivanov, 2021. "Optimal monotone signals in Bayesian persuasion mechanisms," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 72(3), pages 955-1000, October.
    13. Shota Ichihashi & Alex Smolin, 2023. "Buyer-Optimal Algorithmic Recommendations," Papers 2309.12122, arXiv.org, revised Jun 2025.
    14. Agostino Manduchi, 2013. "Non-neutral information costs with match-value uncertainty," Journal of Economics, Springer, vol. 109(1), pages 1-25, May.
    15. 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.
    16. Mensch, Jeffrey, 2021. "Rational inattention and the monotone likelihood ratio property," Journal of Economic Theory, Elsevier, vol. 196(C).
    17. David Lagziel & Ehud Lehrer, 2021. "Dynamic Screening," Working Papers 2101, Ben-Gurion University of the Negev, Department of Economics.
    18. Juan José Ganuza & José S. Penalva, 2006. "On information and competition in private value auctions," Economics Working Papers 937, Department of Economics and Business, Universitat Pompeu Fabra, revised Jul 2006.
    19. Wang, Chengsi, 2011. "Informative Advertising, Consumer Search and Transparency Policy," MPRA Paper 34977, University Library of Munich, Germany.
    20. Ian Jewitt & Daniel Z. Li, 2017. "Cheap Talk Advertising in Auctions: Horizontally vs Vertically Differentiated Products," Department of Economics Working Papers 2017_03, Durham University, Department of Economics.

    More about this item

    Keywords

    ;
    ;
    ;

    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:eee:mateco:v:97:y:2021:i:c:s0304406821001075. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jmateco .

    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.