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Definitions of ambiguous events and the smooth ambiguity model

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  • Peter Klibanoff

    ()

  • Massimo Marinacci

    ()

  • Sujoy Mukerji

    ()

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.
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Suggested Citation

  • 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.
  • Handle: RePEc:spr:joecth:v:48:y:2011:i:2:p:399-424
    DOI: 10.1007/s00199-011-0641-7
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    References listed on IDEAS

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    1. Nehring, Klaus, 1999. "Capacities and probabilistic beliefs: a precarious coexistence," Mathematical Social Sciences, Elsevier, vol. 38(2), pages 197-213, September.
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    8. 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.
    9. 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.
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    11. 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.
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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. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    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. 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.
    11. 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.
    12. 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.
    13. Xiangyu Qu, 2015. "Purely subjective extended Bayesian models with Knightian unambiguity," Theory and Decision, Springer, vol. 79(4), pages 547-571, December.

    More about this item

    Keywords

    Ambiguity; Uncertainty; Knightian uncertainty; Ambiguity aversion; Uncertainty aversion; Ellsberg paradox; D800; D810;

    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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