IDEAS home Printed from https://ideas.repec.org/p/boc/bocoec/954.html
   My bibliography  Save this paper

A Lot of Ambiguity

Author

Listed:
  • Zvi Safra

    (Warwick Business School
    Tel Aviv University)

  • Uzi Segal

    (Boston College)

Abstract

We consider a risk averse decision maker who dislikes ambiguity as in the Ellsberg urns and compare the certainty equivalent of this gamble with the certainty equivalent of the anchoring probabilistic lottery. We deal first with the Choquet EU model and show that un- der some conditions on the capacity nu, when independent ambiguous gambles are repeated and the expected value of the anchoring lot- tery is zero, the difference between the average ambiguous and risky certainty equivalents converges to zero. When the parallel expected value is positive, we show that if the average certainty equivalent of the risky lottery is non-negative, then so is the limit of the average value for the ambiguous model. These results do not extend to the maxmin model or to the smooth recursive model.

Suggested Citation

  • Zvi Safra & Uzi Segal, 2018. "A Lot of Ambiguity," Boston College Working Papers in Economics 954, Boston College Department of Economics, revised 31 Mar 2020.
    • Handle: RePEc:boc:bocoec:954
    as

    Download full text from publisher

    File URL: http://fmwww.bc.edu/EC-P/wp954.pdf
    File Function: main text
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Peter Klibanoff, 2001. "Stochastically independent randomization and uncertainty aversion," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 18(3), pages 605-620.
    2. Yoram Halevy & Vincent Feltkamp, 2005. "A Bayesian Approach to Uncertainty Aversion," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 72(2), pages 449-466.
    3. Liu, Hsin-Hsien & Colman, Andrew M., 2009. "Ambiguity aversion in the long run: Repeated decisions under risk and uncertainty," Journal of Economic Psychology, Elsevier, vol. 30(3), pages 277-284, June.
    4. Robert F. Nau, 2006. "Uncertainty Aversion with Second-Order Utilities and Probabilities," Management Science, INFORMS, vol. 52(1), pages 136-145, January.
    5. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    6. Marinacci, Massimo, 1999. "Limit Laws for Non-additive Probabilities and Their Frequentist Interpretation," Journal of Economic Theory, Elsevier, vol. 84(2), pages 145-195, February.
    7. Jean-Marc Tallon & Alain Chateauneuf, 2002. "Diversification, convex preferences and non-empty core in the Choquet expected utility model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 19(3), pages 509-523.
    8. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    9. Larry G. Epstein & Hiroaki Kaido & Kyoungwon Seo, 2016. "Robust Confidence Regions for Incomplete Models," Econometrica, Econometric Society, vol. 84, pages 1799-1838, September.
    10. Peter Klibanoff & Massimo Marinacci & Sujoy Mukerji, 2005. "A Smooth Model of Decision Making under Ambiguity," Econometrica, Econometric Society, vol. 73(6), pages 1849-1892, November.
    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. Ghirardato, Paolo & Marinacci, Massimo, 2002. "Ambiguity Made Precise: A Comparative Foundation," Journal of Economic Theory, Elsevier, vol. 102(2), pages 251-289, February.
    13. Craig R. Fox & Amos Tversky, 1995. "Ambiguity Aversion and Comparative Ignorance," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 110(3), pages 585-603.
    14. 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.
    15. Ergin, Haluk & Gul, Faruk, 2009. "A theory of subjective compound lotteries," Journal of Economic Theory, Elsevier, vol. 144(3), pages 899-929, May.
    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. Safra, Zvi & Segal, Uzi, 2022. "A lot of ambiguity," Journal of Economic Theory, Elsevier, vol. 200(C).
    2. Johanna Etner & Meglena Jeleva & Jean-Marc Tallon, 2009. "Decision theory under uncertainty," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00429573, HAL.
    3. Mohammed Abdellaoui & Horst Zank, 2023. "Source and rank-dependent utility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 75(4), pages 949-981, May.
    4. Ilke Aydogan & Loic Berger & Valentina Bosetti & Ning Liu, 2018. "Three layers of uncertainty: an experiment," Working Papers 623, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    5. Ilke AYDOGAN & Loïc BERGER & Valentina BOSETTI & Ning LIU, 2022. "Three layers of uncertainty," Working Papers 2022-iRisk-01, IESEG School of Management.
    6. Frick, Mira & Iijima, Ryota & Le Yaouanq, Yves, 2019. "Boolean Representations of Preferences under Ambiguity," Rationality and Competition Discussion Paper Series 173, CRC TRR 190 Rationality and Competition.
    7. Yang, Chun-Lei & Yao, Lan, 2011. "Ellsberg Paradox and Second-order Preference Theories on Ambiguity: Some New Experimental Evidence," MPRA Paper 28531, University Library of Munich, Germany.
    8. Izhakian, Yehuda, 2017. "Expected utility with uncertain probabilities theory," Journal of Mathematical Economics, Elsevier, vol. 69(C), pages 91-103.
    9. repec:hal:journl:hal-03031751 is not listed on IDEAS
    10. Karni, Edi & Maccheroni, Fabio & Marinacci, Massimo, 2015. "Ambiguity and Nonexpected Utility," Handbook of Game Theory with Economic Applications,, Elsevier.
    11. Jewitt, Ian & Mukerji, Sujoy, 2017. "Ordering ambiguous acts," Journal of Economic Theory, Elsevier, vol. 171(C), pages 213-267.
    12. David Ahn & Syngjoo Choi & Douglas Gale & Shachar Kariv, 2014. "Estimating ambiguity aversion in a portfolio choice experiment," Quantitative Economics, Econometric Society, vol. 5, pages 195-223, July.
    13. Evren, Özgür, 2019. "Recursive non-expected utility: Connecting ambiguity attitudes to risk preferences and the level of ambiguity," Games and Economic Behavior, Elsevier, vol. 114(C), pages 285-307.
    14. Michel Grabisch & Benjamin Monet & Vassili Vergopoulos, 2023. "Subjective expected utility through stochastic independence," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(3), pages 723-757, October.
    15. Lang, Matthias & Wambach, Achim, 2013. "The fog of fraud – Mitigating fraud by strategic ambiguity," Games and Economic Behavior, Elsevier, vol. 81(C), pages 255-275.
    16. Madhav Chandrasekher & Mira Frick & Ryota Iijima & Yves Le Yaouanq, 2022. "Dual‐Self Representations of Ambiguity Preferences," Econometrica, Econometric Society, vol. 90(3), pages 1029-1061, May.
    17. Andrew J. Keith & Darryl K. Ahner, 2021. "A survey of decision making and optimization under uncertainty," Annals of Operations Research, Springer, vol. 300(2), pages 319-353, May.
    18. Ilke Aydogan & Loïc Berger & Vincent Théroude, 2023. "More Ambiguous or More Complex? An Investigation of Individual Preferences under Uncertainty," Working Papers of BETA 2023-10, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
    19. Nascimento, Leandro & Riella, Gil, 2011. "A class of incomplete and ambiguity averse preferences," Journal of Economic Theory, Elsevier, vol. 146(2), pages 728-750, March.
    20. Ilke Aydogan & Loïc Berger & Valentina Bosetti & Ning Liu, 2022. "Three layers of uncertainty," Working Papers hal-03031751, HAL.
    21. Veronica Cappelli & Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci & Stefania Minardi, 2021. "Sources of Uncertainty and Subjective Prices," Journal of the European Economic Association, European Economic Association, vol. 19(2), pages 872-912.

    More about this item

    Keywords

    Ellsberg urns; repeated ambiguity; repeated risk; Choquet expected utility; maxmin;
    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:boc:bocoec:954. 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: Christopher F Baum (email available below). General contact details of provider: https://edirc.repec.org/data/debocus.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.