IDEAS home Printed from https://ideas.repec.org/a/eee/jetheo/v154y2014icp604-611.html
   My bibliography  Save this article

Information and the dispersion of posterior expectations

Author

Listed:
  • Brandt, Nikolai
  • Drees, Burkhard
  • Eckwert, Bernhard
  • Várdy, Felix

Abstract

We explore the intuitive idea that more information leads to greater dispersion of posterior beliefs about the expected state of the world. First, we show that two dispersion orders that have been widely used as informativeness criteria do not satisfy the desirable property of ordinality of states (OS), i.e., invariance to increasing monotone state transformations. Then, for the class of monotone information systems, we characterize the weakest information criteria that respect OS and imply the dispersion orders. Our characterizations consist of intuitive conditions on the joint distributions of signals and states. Because of OS, the information criteria induce the dispersion orders not only on the posterior expectations of states, but also of state utilities, under any strictly increasing vNM utility function.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jetheo:v:154:y:2014:i:c:p:604-611
    DOI: 10.1016/j.jet.2014.10.004
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S002205311400146X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jet.2014.10.004?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 search for a different version of it.

    References listed on IDEAS

    as
    1. Moshe Shaked & Miguel A. Sordo & Alfonso Suárez-Llorens, 2012. "Global Dependence Stochastic Orders," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 617-648, September.
    2. 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.
    3. 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.
    4. Kim, Son Ku, 1995. "Efficiency of an Information System in an Agency Model," Econometrica, Econometric Society, vol. 63(1), pages 89-102, January.
    5. Nicola Persico, 2000. "Information Acquisition in Auctions," Econometrica, Econometric Society, vol. 68(1), pages 135-148, January.
    6. 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.
    7. Erin Baker, 2006. "Increasing Risk and Increasing Informativeness: Equivalence Theorems," Operations Research, INFORMS, vol. 54(1), pages 26-36, February.
    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. 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.
    2. 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.
    3. Brandt, Nikolai M. & Eckwert, Bernhard & Várdy, Felix, 2021. "Bayesian learning with variable prior," Journal of Mathematical Economics, Elsevier, vol. 97(C).
    4. Leoni, Patrick & Lundtofte, Frederik, 2017. "Information, stochastic dominance and bidding: The case of Treasury auctions," Economics Letters, Elsevier, vol. 153(C), pages 80-82.
    5. 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.

    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. Brandt, Nikolai M. & Eckwert, Bernhard & Várdy, Felix, 2021. "Bayesian learning with variable prior," Journal of Mathematical Economics, Elsevier, vol. 97(C).
    2. Bernhard Eckwert & Itzhak Zilcha, 2007. "The Effect of Better Information on Income Inequality," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 32(2), pages 287-307, August.
    3. Athey, Susan & Levin, Jonathan, 2018. "The value of information in monotone decision problems," Research in Economics, Elsevier, vol. 72(1), pages 101-116.
    4. Leonardo Rezende, 2018. "Mid-auction information acquisition," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 65(3), pages 751-780, May.
    5. Shi, Xianwen, 2012. "Optimal auctions with information acquisition," Games and Economic Behavior, Elsevier, vol. 74(2), pages 666-686.
    6. Chi, Chang Koo & Olsen, Trond E., 2018. "Relational Incentive Contracts and Performance Measurement," Discussion Papers 2018/6, Norwegian School of Economics, Department of Business and Management Science.
    7. Juan-José Ganuza & Jos Jansen, 2013. "Too Much Information Sharing? Welfare Effects of Sharing Acquired Cost Information in Oligopoly," Journal of Industrial Economics, Wiley Blackwell, vol. 61(4), pages 845-876, December.
    8. Antonio Cabrales & Olivier Gossner & Roberto Serrano, 2012. "The Appeal of Information Transactions," Working Papers 2012-13, Brown University, Department of Economics.
    9. Jacob K. Goeree & Theo Offerman, 2003. "Competitive Bidding in Auctions with Private and Common Values," Economic Journal, Royal Economic Society, vol. 113(489), pages 598-613, July.
    10. Elisa Gerten & Michael Beckmann & Elisa Gerten & Matthias Kräkel, 2022. "Information and Communication Technology, Hierarchy, and Job Design," ECONtribute Discussion Papers Series 189, University of Bonn and University of Cologne, Germany.
    11. Raphael Boleslavsky & Christopher Cotton, 2011. "Learning more by doing less," Working Papers 2012-1, University of Miami, Department of Economics.
    12. Figueroa, Nicolás & Guadalupi, Carla, 2021. "Testing the sender: When signaling is not enough," Journal of Economic Theory, Elsevier, vol. 197(C).
    13. Juan-José Ganuza & José S. Penalva, 2005. "On Information and Competition in Private Value Auctions," Working Papers 158, Barcelona School of Economics.
    14. 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.
    15. Schweizer, Nikolaus & Szech, Nora, 2017. "Revenues and welfare in auctions with information release," Journal of Economic Theory, Elsevier, vol. 170(C), pages 86-111.
    16. Emir Kamenica & Matthew Gentzkow, 2011. "Bayesian Persuasion," American Economic Review, American Economic Association, vol. 101(6), pages 2590-2615, October.
    17. Hao Li & Xianwen Shi, 2017. "Discriminatory Information Disclosure," American Economic Review, American Economic Association, vol. 107(11), pages 3363-3385, November.
    18. Szalay, Dezsö, 2009. "Contracts with endogenous information," Games and Economic Behavior, Elsevier, vol. 65(2), pages 586-625, March.
    19. Li, Yunan, 2019. "Efficient mechanisms with information acquisition," Journal of Economic Theory, Elsevier, vol. 182(C), pages 279-328.
    20. 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.

    More about this item

    Keywords

    Information; Dispersion orderings; Decision making under uncertainty;
    All these keywords.

    JEL classification:

    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

    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:jetheo:v:154:y:2014:i:c:p:604-611. 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/inca/622869 .

    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.