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Definitions of Ambiguous Events and the Smooth Ambiguity Model

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  • Sujoy Mukerji
  • Peter Klibanoff and Massimo Marinacci

Abstract

We examine a variety of preference-based definitions of ambiguous events in the context of the smooth ambiguity model. We first consider the definition proposed in Klibanoff, Marinacci, and Mukerji (2005) based on the classic Ellsberg two-urn paradox (Ellsberg (1961)), and show that it satisfies several desirable properties. We then compare this definition with those of Nehring (1999), Epstein and Zhang (2001), Zhang (2002) and Ghirardato and Marinacci (2002). Within the smooth ambiguity model, we show that Ghirardato and Marinacci (2002) would identify the same set of ambiguous and unambiguous events as our definition while Epstein and Zhang (2001) and Zhang (2002) would yield a different classification. Moreover, we discuss and formally identify two key sources of the differences compared to Epstein and Zhang (2001) and Zhang (2002). The more interesting source is that these two definitions can confound non-constant ambiguity attitude and the ambiguity of an event.

Suggested Citation

  • Sujoy Mukerji & Peter Klibanoff and Massimo Marinacci, 2011. "Definitions of Ambiguous Events and the Smooth Ambiguity Model," Economics Series Working Papers 525, University of Oxford, Department of Economics.
    • Handle: RePEc:oxf:wpaper:525
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    Cited by:

    1. Hideki Iwaki & Yusuke Osaki, 2014. "The dual theory of the smooth ambiguity model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 56(2), pages 275-289, June.
    2. Diederik Aerts & Emmanuel Haven & Sandro Sozzo, 2018. "A proposal to extend expected utility in a quantum probabilistic framework," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 65(4), pages 1079-1109, June.
    3. Robert Nau, 2011. "Risk, ambiguity, and state-preference theory," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(2), pages 437-467, October.
    4. Huang, Yi-Chieh & Tzeng, Larry Y. & Zhao, Lin, 2015. "Comparative ambiguity aversion and downside ambiguity aversion," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 257-269.
    5. Leandro Nascimento & Gil Riella, 2013. "Second-order ambiguous beliefs," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 52(3), pages 1005-1037, April.
    6. Klibanoff, Peter & Mukerji, Sujoy & Seo, Kyoungwon & Stanca, Lorenzo, 2022. "Foundations of ambiguity models under symmetry: α-MEU and smooth ambiguity," Journal of Economic Theory, Elsevier, vol. 199(C).
    7. 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.
    8. 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.
    9. Michele Lombardi & Naoki Yoshihara, 2013. "A full characterization of nash implementation with strategy space reduction," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(1), pages 131-151, September.
    10. Christian Gollier, 2014. "Optimal insurance design of ambiguous risks," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 57(3), pages 555-576, November.
    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. Aloisio Araujo & Alain Chateauneuf & José Faro, 2012. "Pricing rules and Arrow–Debreu ambiguous valuation," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 49(1), pages 1-35, January.
    13. 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.
    14. Xiangyu Qu, 2015. "Purely subjective extended Bayesian models with Knightian unambiguity," Theory and Decision, Springer, vol. 79(4), pages 547-571, December.
    15. Freeman, Mark C. & Groom, Ben, 2016. "How certain are we about the certainty-equivalent long term social discount rate?," Journal of Environmental Economics and Management, Elsevier, vol. 79(C), pages 152-168.

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    JEL classification:

    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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