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What is Ambiguity?

Author

Listed:
  • Massimiliano AMARANTE
Abstract
The concept of Ambiguity designates those situations where the information available to the decision maker is insufficient to form a probabilistic view of the world. Thus, it has provided the motivation for departing from the Subjective Expected Utility (SEU) paradigm. Yet, the formalization of the concept is missing. This is a grave omission as it leaves non-expected utility models hanging on a shaky ground. In particular, it leaves unanswered basic questions such as: (1) Does Ambiguity exist?, (2) If so, which situations should be labeled as "ambiguous"?, (3) Why should one depart from Subjective Expected Utility (SEU) in the presence of Ambiguity?, and (4) If so, what kind of behavior should emerge in the presence of Ambiguity? The present paper fi lls these gaps. Specifically, it identifi es those information structures that are incompatible with SEU theory, and shows that their mathematical properties are the formal counterpart of the intuitive idea of insufficient information. These are used to give a formal definition of Ambiguity and, consequently, to distinguish between ambiguous and unambiguous situations. Finally, the paper shows that behavior not conforming to SEU theory must emerge in correspondence of insufficient information and identifies the class of non-EU models that emerge in the face of Ambiguity. The paper also proposes a new comparative definition of Ambiguity, and discusses its relation with some of the existing literature.

Suggested Citation

  • Massimiliano AMARANTE, 2014. "What is Ambiguity?," Cahiers de recherche 04-2014, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    • Handle: RePEc:mtl:montec:04-2014
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    References listed on IDEAS

    as
    1. Itzhak Gilboa & Massimo Marinacci, 2011. "Ambiguity and the Bayesian Paradigm," Working Papers 379, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    2. Epstein, Larry G. & Schneider, Martin, 2003. "Recursive multiple-priors," Journal of Economic Theory, Elsevier, vol. 113(1), pages 1-31, November.
    3. ,, 2011. "Dynamic choice under ambiguity," Theoretical Economics, Econometric Society, vol. 6(3), September.
    4. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    5. Paolo Ghirardato & Fabio Maccheroni & Massimo Marinacci & Marciano Siniscalchi, 2003. "A Subjective Spin on Roulette Wheels," Econometrica, Econometric Society, vol. 71(6), pages 1897-1908, November.
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    7. Hanany Eran & Klibanoff Peter, 2009. "Updating Ambiguity Averse Preferences," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 9(1), pages 1-53, November.
    8. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    9. Massimo Marinacci, 2002. "Learning from ambiguous urns," Statistical Papers, Springer, vol. 43(1), pages 143-151, January.
    10. Amarante, Massimiliano, 2009. "Foundations of neo-Bayesian statistics," Journal of Economic Theory, Elsevier, vol. 144(5), pages 2146-2173, September.
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    Cited by:

    1. Grabiszewski Konrad, 2016. "On the Rejectability of the Subjective Expected Utility Theory," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 16(2), pages 437-454, June.

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    More about this item

    Keywords

    non-expected utility; information; ambiguity;
    All these keywords.

    JEL classification:

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

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