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Definitions of ambiguous events and the smooth ambiguity model

  • Peter Klibanoff

    ()

  • Massimo Marinacci

    ()

  • Sujoy Mukerji

    ()

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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File URL: http://hdl.handle.net/10.1007/s00199-011-0641-7
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Article provided by Springer in its journal Economic Theory.

Volume (Year): 48 (2011)
Issue (Month): 2 (October)
Pages: 399-424

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Handle: RePEc:spr:joecth:v:48:y:2011:i:2:p:399-424
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  1. Epstein, Larry G & Zhang, Jiankang, 2001. "Subjective Probabilities on Subjectively Unambiguous Events," Econometrica, Econometric Society, vol. 69(2), pages 265-306, March.
  2. Simone Cerreia-Vioglio & Paolo Ghirardato & Fabio Maccheroni & Massimo Marinacci & Marciano Siniscalchi, 2010. "Rational Preferences under Ambiguity," Carlo Alberto Notebooks 169, Collegio Carlo Alberto.
  3. Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini, 2004. "Ambiguity Aversion, Robustness, and the Variational Representation of Preferences," Carlo Alberto Notebooks 12, Collegio Carlo Alberto, revised 2006.
  4. Kopylov, Igor, 2007. "Subjective probabilities on "small" domains," Journal of Economic Theory, Elsevier, vol. 133(1), pages 236-265, March.
  5. Klaus Nehring & Michael Magill & Julian R. Betts, 2003. "Capacities And Probabilistic Beliefs: A Precarious Coexistence," Working Papers 978, University of California, Davis, Department of Economics.
  6. 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.
  7. Epstein, L.G. & Zhang, J., 1998. "Subjective Probabilities on Subjectivity Unambiguous Event," RCER Working Papers 456, University of Rochester - Center for Economic Research (RCER).
  8. Machina,Mark & Schmeidler,David, 1991. "A more robust definition of subjective probability," Discussion Paper Serie A 365, University of Bonn, Germany.
  9. Zhang, Jiankang, 1999. "Qualitative probabilities on [lambda]-systems," Mathematical Social Sciences, Elsevier, vol. 38(1), pages 11-20, July.
  10. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
  11. Sujoy Mukerji & Peter Klibanoff, 2002. "A Smooth Model of Decision,Making Under Ambiguity," Economics Series Working Papers 113, University of Oxford, Department of Economics.
  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. Jiankang Zhang, 1999. "Subjective Ambiguity, Expected Utility and Choquet Expected Utility," Carleton Economic Papers 99-19, Carleton University, Department of Economics, revised Aug 2002.
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