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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.

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Bibliographic Info

Paper provided by University of Oxford, Department of Economics in its series Economics Series Working Papers with number 525.

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Date of creation: 01 Jan 2011
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Handle: RePEc:oxf:wpaper:525

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Keywords: Ambiguity; uncertainty; Knightian uncertainty; ambiguity aversion; uncertainty aversion; Ellsberg paradox;

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References

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  1. Kopylov, Igor, 2007. "Subjective probabilities on "small" domains," Journal of Economic Theory, Elsevier, vol. 133(1), pages 236-265, March.
  2. Zhang, Jiankang, 1999. "Qualitative probabilities on [lambda]-systems," Mathematical Social Sciences, Elsevier, vol. 38(1), pages 11-20, July.
  3. Epstein, L.G. & Zhang, J., 1998. "Subjective Probabilities on Subjectivity Unambiguous Event," RCER Working Papers 456, University of Rochester - Center for Economic Research (RCER).
  4. 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.
  5. Machina,Mark & Schmeidler,David, 1991. "A more robust definition of subjective probability," Discussion Paper Serie A 365, University of Bonn, Germany.
  6. Larry G. Epstein & Jiankang Zhang, 1999. "Subjective Probabilities on Subjectively Unambiguous Events," Carleton Economic Papers 99-18, Carleton University, Department of Economics.
  7. Jiankang Zhang, 2002. "Subjective ambiguity, expected utility and Choquet expected utility," Economic Theory, Springer, vol. 20(1), pages 159-181.
  8. Nehring, Klaus, 1999. "Capacities and probabilistic beliefs: a precarious coexistence," Mathematical Social Sciences, Elsevier, vol. 38(2), pages 197-213, September.
  9. 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.
  10. Simone Cerreia-Vioglio & Paolo Ghirardato & Fabio Maccheroni & Massimo Marinacci & Marciano Siniscalchi, 2011. "Rational preferences under ambiguity," Economic Theory, Springer, vol. 48(2), pages 341-375, October.
  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. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
  13. Ghirardato, Paolo & Marinacci, Massimo, 2002. "Ambiguity Made Precise: A Comparative Foundation," Journal of Economic Theory, Elsevier, vol. 102(2), pages 251-289, February.
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Cited by:
  1. Simone Cerreia-Vioglio & Paolo Ghirardato & Fabio Maccheroni & Massimo Marinacci & Marciano Siniscalchi, 2011. "Rational preferences under ambiguity," Economic Theory, Springer, vol. 48(2), pages 341-375, October.
  2. Leandro Nascimento & Gil Riella, 2013. "Second-order ambiguous beliefs," Economic Theory, Springer, vol. 52(3), pages 1005-1037, April.
  3. 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.
  4. Aloisio Araujo & Alain Chateauneuf & José Faro, 2012. "Pricing rules and Arrow–Debreu ambiguous valuation," Economic Theory, Springer, vol. 49(1), pages 1-35, January.
  5. Alain Chateauneuf & Luciano I. de Castro, 2011. "Ambiguity Aversion and Trade," Discussion Papers 1526, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  6. Hideki Iwaki & Yusuke Osaki, 2014. "The dual theory of the smooth ambiguity model," Economic Theory, Springer, vol. 56(2), pages 275-289, June.
  7. Lombardi Michele & Yoshihara Naoki, 2010. "A Full Characterization of Nash Implementation with Strategy Space Reduction," Research Memorandum 023, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  8. Robert Nau, 2011. "Risk, ambiguity, and state-preference theory," Economic Theory, Springer, vol. 48(2), pages 437-467, October.

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