IDEAS home Printed from https://ideas.repec.org/p/cca/wpaper/169.html
   My bibliography  Save this paper

Rational Preferences under Ambiguity

Author

Listed:
  • Simone Cerreia-Vioglio
  • Paolo Ghirardato
  • Fabio Maccheroni
  • Massimo Marinacci
  • Marciano Siniscalchi

Abstract

This paper analyzes preferences in the presence of ambiguity that are rational in the sense of satisfying the classical ordering condition as well as monotonicity. Under technical conditions that are natural in an Anscombe-Aumann environment, we show that even for such general preference model it is possible to identify a set of priors, as first envisioned by Ellsberg (1961). We then discuss ambiguity attitudes, as well as unambiguous acts and events, for the class of rational preferences we consider.

Suggested Citation

  • Simone Cerreia-Vioglio & Paolo Ghirardato & Fabio Maccheroni & Massimo Marinacci & Marciano Siniscalchi, 2010. "Rational Preferences under Ambiguity," Carlo Alberto Notebooks 169, Collegio Carlo Alberto.
    • Handle: RePEc:cca:wpaper:169
    as

    Download full text from publisher

    File URL: https://www.carloalberto.org/wp-content/uploads/2018/11/no.169.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    • Simone Cerreia-Vioglio & Paolo Ghirardato & Fabio Maccheroni & Massimo Marinacci & Marciano Siniscalchi, 2011. "Rational preferences under ambiguity," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(2), pages 341-375, October.

    References listed on IDEAS

    as
    1. Peter Klibanoff & Massimo Marinacci & Sujoy Mukerji, 2011. "Definitions of ambiguous events and the smooth ambiguity model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(2), pages 399-424, October.
    2. 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.
    3. Kopylov, Igor, 2007. "Subjective probabilities on "small" domains," Journal of Economic Theory, Elsevier, vol. 133(1), pages 236-265, March.
    4. 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.
    5. Cerreia-Vioglio, S. & Maccheroni, F. & Marinacci, M. & Montrucchio, L., 2011. "Uncertainty averse preferences," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1275-1330, July.
    6. Klaus Nehring, 2006. "Bernoulli Without Bayes: A Theory of Utility-Sophisticated Preferences under Ambiguity," Economics Working Papers 0072, Institute for Advanced Study, School of Social Science.
    7. Klaus Nehring, 2006. "Is it Possible to Define Subjective Probabilities in Purely Behavioral Terms? A Comment on Epstein-Zhang (2001)," Economics Working Papers 0067, Institute for Advanced Study, School of Social Science.
    8. Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo, 2005. "Certainty Independence and the Separation of Utility and Beliefs," Journal of Economic Theory, Elsevier, vol. 120(1), pages 129-136, January.
    9. Nehring, Klaus, 1999. "Capacities and probabilistic beliefs: a precarious coexistence," Mathematical Social Sciences, Elsevier, vol. 38(2), pages 197-213, September.
    10. Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo, 2004. "Differentiating ambiguity and ambiguity attitude," Journal of Economic Theory, Elsevier, vol. 118(2), pages 133-173, October.
    11. Itzhak Gilboa & Fabio Maccheroni & Massimo Marinacci & David Schmeidler, 2010. "Objective and Subjective Rationality in a Multiple Prior Model," Econometrica, Econometric Society, vol. 78(2), pages 755-770, March.
    12. 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.
    13. Epstein, Larry G & Zhang, Jiankang, 2001. "Subjective Probabilities on Subjectively Unambiguous Events," Econometrica, Econometric Society, vol. 69(2), pages 265-306, March.
    14. Tomasz, Strzalecki, 2011. "Probabilistic sophistication and variational preferences," Journal of Economic Theory, Elsevier, vol. 146(5), pages 2117-2125, September.
    15. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    16. 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.
    17. Marciano Siniscalchi, 2009. "Vector Expected Utility and Attitudes Toward Variation," Econometrica, Econometric Society, vol. 77(3), pages 801-855, May.
    18. Massimo Marinacci, 2002. "Probabilistic Sophistication and Multiple Priors," Econometrica, Econometric Society, vol. 70(2), pages 755-764, March.
    19. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    20. Machina, Mark J & Schmeidler, David, 1992. "A More Robust Definition of Subjective Probability," Econometrica, Econometric Society, vol. 60(4), pages 745-780, July.
    21. Ghirardato, Paolo & Marinacci, Massimo, 2002. "Ambiguity Made Precise: A Comparative Foundation," Journal of Economic Theory, Elsevier, vol. 102(2), pages 251-289, February.
    22. Larry G. Epstein, 1999. "A Definition of Uncertainty Aversion," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(3), pages 579-608.
    23. 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.
    24. Nehring, Klaus, 2009. "Imprecise probabilistic beliefs as a context for decision-making under ambiguity," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1054-1091, May.
    25. Paolo Ghirardato & Marciano Siniscalchi, 2010. "A more robust definition of multiple priors," Carlo Alberto Notebooks 144, Collegio Carlo Alberto.
    26. Epstein, L.G. & Zhang, J., 1998. "Subjective Probabilities on Subjectivity Unambiguous Event," RCER Working Papers 456, University of Rochester - Center for Economic Research (RCER).
    27. Amarante, Massimiliano & Filiz, Emel, 2007. "Ambiguous events and maxmin expected utility," Journal of Economic Theory, Elsevier, vol. 134(1), pages 1-33, 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. Borie, Dino, 2023. "Maxmin expected utility in Savage's framework," Journal of Economic Theory, Elsevier, vol. 210(C).
    2. Xiangyu Qu, 2015. "Purely subjective extended Bayesian models with Knightian unambiguity," Theory and Decision, Springer, vol. 79(4), pages 547-571, December.
    3. Jewitt, Ian & Mukerji, Sujoy, 2017. "Ordering ambiguous acts," Journal of Economic Theory, Elsevier, vol. 171(C), pages 213-267.
    4. Klaus Nehring, 2006. "Decision-Making in the Context of Imprecise Probabilistic Beliefs," Economics Working Papers 0034, Institute for Advanced Study, School of Social Science.
    5. Peter Klibanoff & Sujoy Mukerji & Kyoungwon Seo, 2014. "Perceived Ambiguity and Relevant Measures," Econometrica, Econometric Society, vol. 82(5), pages 1945-1978, September.
    6. André, Eric, 2016. "Crisp monetary acts in multiple-priors models of decision under ambiguity," Journal of Mathematical Economics, Elsevier, vol. 67(C), pages 153-161.
    7. 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.
    8. Qu, Xiangyu, 2013. "Maxmin expected utility with additivity on unambiguous events," Journal of Mathematical Economics, Elsevier, vol. 49(3), pages 245-249.
    9. Nehring, Klaus, 2009. "Imprecise probabilistic beliefs as a context for decision-making under ambiguity," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1054-1091, May.
    10. Klaus Nehring, 2006. "Bernoulli Without Bayes: A Theory of Utility-Sophisticated Preferences under Ambiguity," Economics Working Papers 0072, Institute for Advanced Study, School of Social Science.
    11. Alain Chateauneuf & Luciano De Castro, 2011. "Ambiguity Aversion and Absence of Trade," Discussion Papers 1535, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    12. Xiangyu Qu, 2015. "A belief-based definition of ambiguity aversion," Theory and Decision, Springer, vol. 79(1), pages 15-30, July.
    13. Luciano Castro & Alain Chateauneuf, 2011. "Ambiguity aversion and trade," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(2), pages 243-273, October.
    14. Cerreia-Vioglio, Simone & Maccheroni, Fabio & Marinacci, Massimo & Montrucchio, Luigi, 2012. "Probabilistic sophistication, second order stochastic dominance and uncertainty aversion," Journal of Mathematical Economics, Elsevier, vol. 48(5), pages 271-283.
    15. Karni, Edi & Maccheroni, Fabio & Marinacci, Massimo, 2015. "Ambiguity and Nonexpected Utility," Handbook of Game Theory with Economic Applications,, Elsevier.
    16. Dominiak, Adam & Duersch, Peter & Lefort, Jean-Philippe, 2012. "A dynamic Ellsberg urn experiment," Games and Economic Behavior, Elsevier, vol. 75(2), pages 625-638.
    17. Ghirardato, Paolo & Siniscalchi, Marciano, 2018. "Risk sharing in the small and in the large," Journal of Economic Theory, Elsevier, vol. 175(C), pages 730-765.
    18. Chew, Soo Hong & Sagi, Jacob S., 2008. "Small worlds: Modeling attitudes toward sources of uncertainty," Journal of Economic Theory, Elsevier, vol. 139(1), pages 1-24, March.
    19. Yehuda Izhakian & Zur Izhakian, 2015. "Decision making in phantom spaces," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 58(1), pages 59-98, January.
    20. Brian Hill, 2009. "Confidence and ambiguity," Working Papers hal-00489870, HAL.

    More about this item

    Keywords

    Rational Preferences; Ambiguity; Unambiguous Acts and Events;
    All these keywords.

    JEL classification:

    • 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:cca:wpaper:169. 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: Giovanni Bert (email available below). General contact details of provider: https://edirc.repec.org/data/fccaait.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.