IDEAS home Printed from https://ideas.repec.org/p/bge/wpaper/1424.html
   My bibliography  Save this paper

Updating Under Imprecise Information

Author

Listed:
  • Yi-Hsuan Lin
  • Fernando Payró Chew

Abstract

This paper models an agent that ranks actions with uncertain payoffs after observing a signal that could have been generated by multiple objective information structures. Under the assumption that the agent’s preferences conform to the multiple priors model (Gilboa and Schmeidler (1989)), we show that a simple behavioral axiom characterizes a generalization of Bayesian Updating. Our axiom requires that whenever all possible sources of information agree that it is more ’likely’ for an action with uncertain payoffs to be better than one with certain payoffs, the agent prefers the former. We also provide axiomatizations for several special cases. Finally, we consider the situation where the informational content of a signal is purely subjective. We characterize the existence of a subjective set of information structures under full Bayesian updating for two extreme cases: (i) No ex-ante state ambiguity, and (ii) No signal ambiguity.

Suggested Citation

  • Yi-Hsuan Lin & Fernando Payró Chew, 2024. "Updating Under Imprecise Information," Working Papers 1424, Barcelona School of Economics.
    • Handle: RePEc:bge:wpaper:1424
    as

    Download full text from publisher

    File URL: https://bse.eu/sites/default/files/working_paper_pdfs/1424.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Gilboa Itzhak & Schmeidler David, 1993. "Updating Ambiguous Beliefs," Journal of Economic Theory, Elsevier, vol. 59(1), pages 33-49, February.
    2. Larry G. Epstein & Martin Schneider, 2010. "Ambiguity and Asset Markets," Annual Review of Financial Economics, Annual Reviews, vol. 2(1), pages 315-346, December.
    3. Kellner, Christian & Le Quement, Mark T., 2018. "Endogenous ambiguity in cheap talk," Journal of Economic Theory, Elsevier, vol. 173(C), pages 1-17.
    4. Matthew Kovach, 2021. "Ambiguity and Partial Bayesian Updating," Papers 2102.11429, arXiv.org, revised Mar 2023.
    5. Cheng, Xiaoyu, 2022. "Relative Maximum Likelihood updating of ambiguous beliefs," Journal of Mathematical Economics, Elsevier, vol. 99(C).
    6. Larry G. Epstein & Martin Schneider, 2007. "Learning Under Ambiguity," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 74(4), pages 1275-1303.
    7. José Heleno Faro & Jean-Philippe Lefort, 2019. "Dynamic objective and subjective rationality," Post-Print hal-04233768, HAL.
    8. David S. Ahn, 2008. "Ambiguity Without a State Space," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 75(1), pages 3-28.
    9. Gajdos, T. & Hayashi, T. & Tallon, J.-M. & Vergnaud, J.-C., 2008. "Attitude toward imprecise information," Journal of Economic Theory, Elsevier, vol. 140(1), pages 27-65, May.
    10. Riedel, Frank & Tallon, Jean-Marc & Vergopoulos, Vassili, 2018. "Dynamically consistent preferences under imprecise probabilistic information," Journal of Mathematical Economics, Elsevier, vol. 79(C), pages 117-124.
    11. Faro, José Heleno & Lefort, Jean-Philippe, 2019. "Dynamic objective and subjective rationality," Theoretical Economics, Econometric Society, vol. 14(1), January.
    12. Paolo Ghirardato, 2002. "Revisiting Savage in a conditional world," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 20(1), pages 83-92.
    13. Matthew Rabin & Joel L. Schrag, 1999. "First Impressions Matter: A Model of Confirmatory Bias," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 114(1), pages 37-82.
    14. Gul, Faruk & Pesendorfer, Wolfgang, 2021. "Evaluating ambiguous random variables from Choquet to maxmin expected utility," Journal of Economic Theory, Elsevier, vol. 192(C).
    15. Wojciech Olszewski, 2007. "Preferences Over Sets of Lotteries -super-1," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 74(2), pages 567-595.
    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. Lorenzo Bastianello & José Heleno Faro & Ana Santos, 2022. "Dynamically consistent objective and subjective rationality," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 74(2), pages 477-504, September.
    2. Larry G Epstein & Yoram Halevy, 2024. "Hard-to-Interpret Signals," Journal of the European Economic Association, European Economic Association, vol. 22(1), pages 393-427.
    3. Cheng, Xiaoyu, 2022. "Relative Maximum Likelihood updating of ambiguous beliefs," Journal of Mathematical Economics, Elsevier, vol. 99(C).
    4. Beauchêne, Dorian & Li, Jian & Li, Ming, 2019. "Ambiguous persuasion," Journal of Economic Theory, Elsevier, vol. 179(C), pages 312-365.
    5. Hill, Brian, 2022. "Updating confidence in beliefs," Journal of Economic Theory, Elsevier, vol. 199(C).
    6. Minardi, Stefania & Savochkin, Andrei, 2019. "Subjective contingencies and limited Bayesian updating," Journal of Economic Theory, Elsevier, vol. 183(C), pages 1-45.
    7. Aurélien Baillon & Han Bleichrodt & Umut Keskin & Olivier l’Haridon & Chen Li, 2018. "The Effect of Learning on Ambiguity Attitudes," Management Science, INFORMS, vol. 64(5), pages 2181-2198, May.
    8. Lorenzo Bastianello & Jos'e Heleno Faro & Ana Santos, 2020. "Dynamically Consistent Objective and Subjective Rationality," Papers 2004.12347, arXiv.org.
    9. Philipp K. Illeditsch & Jayant V. Ganguli & Scott Condie, 2021. "Information Inertia," Journal of Finance, American Finance Association, vol. 76(1), pages 443-479, February.
    10. Hill, Brian, 2020. "Dynamic consistency and ambiguity: A reappraisal," Games and Economic Behavior, Elsevier, vol. 120(C), pages 289-310.
    11. Aurélien Baillon & Han Bleichrodt & Umut Keskin & Olivier L'Haridon & Author-Name: Chen Li, 2013. "Learning under ambiguity: An experiment using initial public offerings on a stock market," Economics Working Paper Archive (University of Rennes & University of Caen) 201331, Center for Research in Economics and Management (CREM), University of Rennes, University of Caen and CNRS.
    12. ,, 2014. "Second order beliefs models of choice under imprecise risk: non-additive second order beliefs vs. nonlinear second order utility," Theoretical Economics, Econometric Society, vol. 9(3), September.
    13. Federica Ceron & Vassili Vergopoulos, 2020. "Recursive objective and subjective multiple priors," Post-Print halshs-02900497, HAL.
    14. Jewitt, Ian & Mukerji, Sujoy, 2017. "Ordering ambiguous acts," Journal of Economic Theory, Elsevier, vol. 171(C), pages 213-267.
    15. Gérard Mondello, 2022. "Information Source's Reliability," GREDEG Working Papers 2022-21, Groupe de REcherche en Droit, Economie, Gestion (GREDEG CNRS), Université Côte d'Azur, France, revised Oct 2022.
    16. Chambers, Christopher P. & Hayashi, Takashi, 2010. "Bayesian consistent belief selection," Journal of Economic Theory, Elsevier, vol. 145(1), pages 432-439, January.
    17. Groneck, Max & Ludwig, Alexander & Zimper, Alexander, 2016. "A life-cycle model with ambiguous survival beliefs," Journal of Economic Theory, Elsevier, vol. 162(C), pages 137-180.
    18. Marciano Siniscalchi, 2009. "Vector Expected Utility and Attitudes Toward Variation," Econometrica, Econometric Society, vol. 77(3), pages 801-855, May.
    19. Raphaël Giraud & Jean-Marc Tallon, 2011. "Are beliefs a matter of taste? A case for objective imprecise information," Theory and Decision, Springer, vol. 71(1), pages 23-31, July.
    20. Alexander Ludwig & Alexander Zimper, 2013. "A decision-theoretic model of asset-price underreaction and overreaction to dividend news," Annals of Finance, Springer, vol. 9(4), pages 625-665, November.

    More about this item

    Keywords

    updating; ambiguity; imprecise information; MaxMin;
    All these keywords.

    JEL classification:

    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory

    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:bge:wpaper:1424. 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: Bruno Guallar (email available below). General contact details of provider: https://edirc.repec.org/data/bargses.html .

    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.