IDEAS home Printed from https://ideas.repec.org/p/kyo/wpaper/935.html
   My bibliography  Save this paper

Bayesian Updating for Complementarily Additive Beliefs under Ambiguity

Author

Listed:
  • Mayumi Horie

    () (Hiroshima University of Economics)

Abstract

This paper proposes a formal characterization of extended Bayesian updating for complementarily additive subjective beliefs under ambiguity, which are compatible with a wide range of choice behavior toward ambiguity. The main result shows that, based on the biseparability of Ghirardato and Marinacci (2001), extended Bayesian updating characterizes the update rule which is a step-by-step composite updating for priors, where one of Dempster-Shafer rule, Bayes'update rule and Fagin-Halpern rule is applied to each step. As applications, more speci c preference relations are examined, such as the maxmin expected utility, the rank-dependent expected utility, and the concave expected utility preferences by Lehrer (2009).

Suggested Citation

  • Mayumi Horie, 2016. "Bayesian Updating for Complementarily Additive Beliefs under Ambiguity," KIER Working Papers 935, Kyoto University, Institute of Economic Research.
  • Handle: RePEc:kyo:wpaper:935
    as

    Download full text from publisher

    File URL: http://www.kier.kyoto-u.ac.jp/DP/DP935.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Aurelien Baillon & Olivier L'Haridon & Laetitia Placido, 2011. "Ambiguity Models and the Machina Paradoxes," American Economic Review, American Economic Association, vol. 101(4), pages 1547-1560, June.
    2. Grant, Simon & Kajii, Atsushi & Polak, Ben, 2000. "Decomposable Choice under Uncertainty," Journal of Economic Theory, Elsevier, vol. 92(2), pages 169-197, June.
    3. Hanany, Eran & Klibanoff, Peter, 2007. "Updating preferences with multiple priors," Theoretical Economics, Econometric Society, vol. 2(3), September.
    4. Gilboa Itzhak & Schmeidler David, 1993. "Updating Ambiguous Beliefs," Journal of Economic Theory, Elsevier, vol. 59(1), pages 33-49, February.
    5. Hong Chew Soo & Epstein Larry G. & Wakker Peter, 1993. "A Unifying Approach to Axiomatic Non-expected Utility Theories: Correction and Comment," Journal of Economic Theory, Elsevier, vol. 59(1), pages 183-188, February.
    6. Yaarit Even & Ehud Lehrer, 2014. "Decomposition-integral: unifying Choquet and the concave integrals," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 56(1), pages 33-58, May.
    7. 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.
    8. Cesaltina Pacheco Pires, 2002. "A Rule For Updating Ambiguous Beliefs," Theory and Decision, Springer, vol. 53(2), pages 137-152, September.
    9. Casadesus-Masanell, Ramon & Klibanoff, Peter & Ozdenoren, Emre, 2000. "Maxmin Expected Utility over Savage Acts with a Set of Priors," Journal of Economic Theory, Elsevier, vol. 92(1), pages 35-65, May.
    10. Siniscalchi, Marciano, 2011. "Dynamic choice under ambiguity," Theoretical Economics, Econometric Society, vol. 6(3), September.
    11. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    12. Nakamura, Yutaka, 1990. "Subjective expected utility with non-additive probabilities on finite state spaces," Journal of Economic Theory, Elsevier, vol. 51(2), pages 346-366, August.
    13. Alon, Shiri & Schmeidler, David, 2014. "Purely subjective Maxmin Expected Utility," Journal of Economic Theory, Elsevier, vol. 152(C), pages 382-412.
    14. Mark J. Machina, 2014. "Ambiguity Aversion with Three or More Outcomes," American Economic Review, American Economic Association, vol. 104(12), pages 3814-3840, December.
    15. Gilboa, Itzhak, 1987. "Expected utility with purely subjective non-additive probabilities," Journal of Mathematical Economics, Elsevier, vol. 16(1), pages 65-88, February.
    16. Daniel Ellsberg, 1961. "Risk, Ambiguity, and the Savage Axioms," The Quarterly Journal of Economics, Oxford University Press, vol. 75(4), pages 643-669.
    17. Gul, Faruk, 1991. "A Theory of Disappointment Aversion," Econometrica, Econometric Society, vol. 59(3), pages 667-686, May.
    18. Ramon Casadesus-Masanell & Peter Klibanoff & Emre Ozdenoren, 1998. "Maximum Expected Utility over Savage Acts with a Set of Priors," Discussion Papers 1218, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    19. Mayumi Horie, 2007. "A General Update Rule for Convex Capacities," KIER Working Papers 644, Kyoto University, Institute of Economic Research.
    20. Gul, Faruk & Pesendorfer, Wolfgang, 2015. "Hurwicz expected utility and subjective sources," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 465-488.
    21. Horie, Mayumi, 2013. "Reexamination on updating Choquet beliefs," Journal of Mathematical Economics, Elsevier, vol. 49(6), pages 467-470.
    22. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    23. Chew, S. H. & Epstein, L. G., 1989. "A unifying approach to axiomatic non-expected utility theories," Journal of Economic Theory, Elsevier, vol. 49(2), pages 207-240, December.
    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. Alexander Zimper, 2011. "Do Bayesians Learn Their Way Out of Ambiguity?," Decision Analysis, INFORMS, vol. 8(4), pages 269-285, December.
    2. Faro, José Heleno & Lefort, Jean-Philippe, 2019. "Dynamic objective and subjective rationality," Theoretical Economics, Econometric Society, vol. 14(1), January.
    3. 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.
    4. André Lapied & Pascal Tocquebeuf, 2007. "Consistent Dynamice Choice And Non-Expected Utility Preferences," Working Papers halshs-00353880, HAL.
    5. Daniel Heyen, 2018. "Ambiguity aversion under maximum-likelihood updating," Theory and Decision, Springer, vol. 84(3), pages 373-386, May.
    6. 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.
    7. Dominiak, Adam & Duersch, Peter & Lefort, Jean-Philippe, 2012. "A dynamic Ellsberg urn experiment," Games and Economic Behavior, Elsevier, vol. 75(2), pages 625-638.
    8. 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.
    9. repec:dau:papers:123456789/7323 is not listed on IDEAS
    10. Paolo Ghirardato & Massimo Marinacci, 2001. "Risk, Ambiguity, and the Separation of Utility and Beliefs," Mathematics of Operations Research, INFORMS, vol. 26(4), pages 864-890, November.
    11. Xiangyu Qu, 2015. "Purely subjective extended Bayesian models with Knightian unambiguity," Theory and Decision, Springer, vol. 79(4), pages 547-571, December.
    12. Galanis, S., 2019. "Dynamic Consistency, Valuable Information and Subjective Beliefs," Working Papers 19/02, Department of Economics, City University London.
    13. Zimper, Alexander, 2009. "Half empty, half full and why we can agree to disagree forever," Journal of Economic Behavior & Organization, Elsevier, vol. 71(2), pages 283-299, August.
    14. Chambers, Robert G. & Melkonyan, Tigran, 2009. "Smoothing preference kinks with information," Mathematical Social Sciences, Elsevier, vol. 58(2), pages 173-189, September.
    15. Adam Dominiak & Jean-Philippe Lefort, 2011. "Unambiguous events and dynamic Choquet preferences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 46(3), pages 401-425, April.
    16. Xiaoyu Cheng, 2019. "Relative Maximum Likelihood Updating of Ambiguous Beliefs," Papers 1911.02678, arXiv.org, revised Jan 2021.
    17. Takao Asano & Hiroyuki Kojima, 2018. "Consequentialism and Dynamic Consistency in Updating Ambiguous Beliefs," KIER Working Papers 987, Kyoto University, Institute of Economic Research.
    18. Li, Jian, 0. "Preferences for partial information and ambiguity," Theoretical Economics, Econometric Society.
    19. Giulianella Coletti & Davide Petturiti & Barbara Vantaggi, 2019. "Dutch book rationality conditions for conditional preferences under ambiguity," Annals of Operations Research, Springer, vol. 279(1), pages 115-150, August.
    20. Hill, Brian, 2020. "Dynamic consistency and ambiguity: A reappraisal," Games and Economic Behavior, Elsevier, vol. 120(C), pages 289-310.
    21. Dominiak, Adam & Lefort, Jean-Philippe, 2015. "“Agreeing to disagree” type results under ambiguity," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 119-129.

    More about this item

    Keywords

    ambiguous belief; Bayesian update rule; multiple priors; non-additive measure; subjective probability; biseparable preference;
    All these keywords.

    JEL classification:

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

    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:kyo:wpaper:935. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Chiaki Hara). General contact details of provider: https://edirc.repec.org/data/iekyojp.html .

    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 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.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.