IDEAS home Printed from https://ideas.repec.org/a/eee/mateco/v99y2022ics0304406821001488.html
   My bibliography  Save this article

Relative Maximum Likelihood updating of ambiguous beliefs

Author

Listed:
  • Cheng, Xiaoyu

Abstract

This paper proposes and axiomatizes a new updating rule: Relative Maximum Likelihood (RML) updating for ambiguous beliefs represented by a set of priors (C). This rule takes the form of applying Bayes’ rule to a subset of C. This subset is a linear contraction of C towards its subset ascribing the maximal probability to the observed event. The degree of contraction captures the extent of willingness to discard priors based on likelihood when updating. Two well-known updating rules of multiple priors, full Bayesian (FB) and Maximum Likelihood (ML), are included as special cases of RML. An axiomatic characterization of conditional preferences generated by RML updating is provided when the preferences admit Maxmin Expected Utility representations. The axiomatization relies on weakening the axioms characterizing FB and ML. The axiom characterizing ML is identified for the first time in this paper, addressing a long-standing open question in the literature.

Suggested Citation

  • Cheng, Xiaoyu, 2022. "Relative Maximum Likelihood updating of ambiguous beliefs," Journal of Mathematical Economics, Elsevier, vol. 99(C).
    • Handle: RePEc:eee:mateco:v:99:y:2022:i:c:s0304406821001488
    DOI: 10.1016/j.jmateco.2021.102587
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304406821001488
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmateco.2021.102587?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. repec:dau:papers:123456789/7333 is not listed on IDEAS
    2. Emir Kamenica & Matthew Gentzkow, 2011. "Bayesian Persuasion," American Economic Review, American Economic Association, vol. 101(6), pages 2590-2615, October.
    3. Gilboa Itzhak & Schmeidler David, 1993. "Updating Ambiguous Beliefs," Journal of Economic Theory, Elsevier, vol. 59(1), pages 33-49, February.
    4. 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.
    5. De Filippis, Roberta & Guarino, Antonio & Jehiel, Philippe & Kitagawa, Toru, 2022. "Non-Bayesian updating in a social learning experiment," Journal of Economic Theory, Elsevier, vol. 199(C).
    6. ,, 2011. "Dynamic choice under ambiguity," Theoretical Economics, Econometric Society, vol. 6(3), September.
    7. Gul, Faruk & Pesendorfer, Wolfgang, 2021. "Evaluating ambiguous random variables from Choquet to maxmin expected utility," Journal of Economic Theory, Elsevier, vol. 192(C).
    8. Siniscalchi, Marciano, 2006. "A behavioral characterization of plausible priors," Journal of Economic Theory, Elsevier, vol. 128(1), pages 91-135, May.
    9. Subir Bose & Ludovic Renou, 2014. "Mechanism Design With Ambiguous Communication Devices," Econometrica, Econometric Society, vol. 82(5), pages 1853-1872, September.
    10. Brian Hill, 2022. "Updating confidence in beliefs," Post-Print hal-03503986, HAL.
    11. Dominiak, Adam & Duersch, Peter & Lefort, Jean-Philippe, 2012. "A dynamic Ellsberg urn experiment," Games and Economic Behavior, Elsevier, vol. 75(2), pages 625-638.
    12. Beauchêne, Dorian & Li, Jian & Li, Ming, 2019. "Ambiguous persuasion," Journal of Economic Theory, Elsevier, vol. 179(C), pages 312-365.
    13. Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini, 2006. "Ambiguity Aversion, Robustness, and the Variational Representation of Preferences," Econometrica, Econometric Society, vol. 74(6), pages 1447-1498, November.
    14. Pietro Ortoleva, 2014. "Hypothesis Testing and Ambiguity Aversion," Rivista di Politica Economica, SIPI Spa, issue 3, pages 45-64, July-Sept.
    15. 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.
    16. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    17. Machina, Mark J & Schmeidler, David, 1992. "A More Robust Definition of Subjective Probability," Econometrica, Econometric Society, vol. 60(4), pages 745-780, July.
    18. Li, Jian, 2020. "Preferences for partial information and ambiguity," Theoretical Economics, Econometric Society, vol. 15(3), July.
    19. Georgalos, Konstantinos, 2021. "Dynamic decision making under ambiguity: An experimental investigation," Games and Economic Behavior, Elsevier, vol. 127(C), pages 28-46.
    20. , & ,, 2007. "Updating preferences with multiple priors," Theoretical Economics, Econometric Society, vol. 2(3), September.
    21. Pietro Ortoleva, 2012. "Modeling the Change of Paradigm: Non-Bayesian Reactions to Unexpected News," American Economic Review, American Economic Association, vol. 102(6), pages 2410-2436, October.
    22. Xiaoyu Cheng, 2021. "Extended Relative Maximum Likelihood Updating of Choquet Beliefs," Papers 2109.02597, arXiv.org.
    23. Epstein, Larry G. & Schneider, Martin, 2003. "Recursive multiple-priors," Journal of Economic Theory, Elsevier, vol. 113(1), pages 1-31, November.
    24. Cesaltina Pacheco Pires, 2002. "A Rule For Updating Ambiguous Beliefs," Theory and Decision, Springer, vol. 53(2), pages 137-152, September.
    25. repec:dau:papers:123456789/7357 is not listed on IDEAS
    26. Daniel Ellsberg, 1961. "Risk, Ambiguity, and the Savage Axioms," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 75(4), pages 643-669.
    27. Kellner, Christian & Le Quement, Mark T., 2018. "Endogenous ambiguity in cheap talk," Journal of Economic Theory, Elsevier, vol. 173(C), pages 1-17.
    28. Hanany Eran & Klibanoff Peter, 2009. "Updating Ambiguity Averse Preferences," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 9(1), pages 1-53, November.
    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. Phoebe Koundouri & Nikitas Pittis & Panagiotis Samartzis, 2023. "Counterfactual Priors: A Bayesian Response to Ellsberg's Paradox," DEOS Working Papers 2307, Athens University of Economics and Business.
    2. Yi-Hsuan Lin & Fernando Payró Chew, 2024. "Updating Under Imprecise Information," Working Papers 1424, Barcelona School of Economics.

    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. Xiaoyu Cheng, 2019. "Relative Maximum Likelihood Updating of Ambiguous Beliefs," Papers 1911.02678, arXiv.org, revised Oct 2021.
    2. Konstantinos Georgalos, 2019. "An experimental test of the predictive power of dynamic ambiguity models," Journal of Risk and Uncertainty, Springer, vol. 59(1), pages 51-83, August.
    3. Georgalos, Konstantinos, 2021. "Dynamic decision making under ambiguity: An experimental investigation," Games and Economic Behavior, Elsevier, vol. 127(C), pages 28-46.
    4. Hill, Brian, 2022. "Updating confidence in beliefs," Journal of Economic Theory, Elsevier, vol. 199(C).
    5. Daniel Heyen, 2018. "Ambiguity aversion under maximum-likelihood updating," Theory and Decision, Springer, vol. 84(3), pages 373-386, May.
    6. Heyen, Daniel, 2018. "Ambiguity aversion under maximum-likelihood updating," LSE Research Online Documents on Economics 80342, London School of Economics and Political Science, LSE Library.
    7. Alexander Zimper, 2011. "Do Bayesians Learn Their Way Out of Ambiguity?," Decision Analysis, INFORMS, vol. 8(4), pages 269-285, December.
    8. Beauchêne, Dorian & Li, Jian & Li, Ming, 2019. "Ambiguous persuasion," Journal of Economic Theory, Elsevier, vol. 179(C), pages 312-365.
    9. Gumen, Anna & Savochkin, Andrei, 2013. "Dynamically stable preferences," Journal of Economic Theory, Elsevier, vol. 148(4), pages 1487-1508.
    10. Hill, Brian, 2020. "Dynamic consistency and ambiguity: A reappraisal," Games and Economic Behavior, Elsevier, vol. 120(C), pages 289-310.
    11. Spyros Galanis, 2021. "Dynamic consistency, valuable information and subjective beliefs," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(4), pages 1467-1497, June.
    12. Dominiak, Adam & Duersch, Peter & Lefort, Jean-Philippe, 2012. "A dynamic Ellsberg urn experiment," Games and Economic Behavior, Elsevier, vol. 75(2), pages 625-638.
    13. Xiaoyu Cheng, 2020. "Ambiguous Persuasion: An Ex-Ante Formulation," Papers 2010.05376, arXiv.org, revised Nov 2023.
    14. Shishkin, Denis & Ortoleva, Pietro, 2023. "Ambiguous information and dilation: An experiment," Journal of Economic Theory, Elsevier, vol. 208(C).
    15. Auster, Sarah & Kellner, Christian, 2022. "Robust bidding and revenue in descending price auctions," Journal of Economic Theory, Elsevier, vol. 199(C).
    16. Kathleen Ngangoué, M., 2021. "Learning under ambiguity: An experiment in gradual information processing," Journal of Economic Theory, Elsevier, vol. 195(C).
    17. Bleichrodt, Han & Eichberger, Jürgen & Grant, Simon & Kelsey, David & Li, Chen, 2021. "Testing dynamic consistency and consequentialism under ambiguity," European Economic Review, Elsevier, vol. 134(C).
    18. Rui Tang, 2020. "A Theory of Updating Ambiguous Information," Papers 2012.13650, arXiv.org.
    19. Faro, José Heleno & Lefort, Jean-Philippe, 2019. "Dynamic objective and subjective rationality," Theoretical Economics, Econometric Society, vol. 14(1), January.
    20. Takao Asano & Hiroyuki Kojima, 2019. "Consequentialism and dynamic consistency in updating ambiguous beliefs," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 68(1), pages 223-250, July.

    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:99:y:2022:i:c:s0304406821001488. 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.