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Rational Preferences under Ambiguity

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  • Simone Cerreia-Vioglio
  • Paolo Ghirardato
  • Fabio Maccheroni
  • Massimo Marinacci
  • Marciano Siniscalchi

Abstract

This paper analyzes preferences in the presence of ambiguity that are rational in the sense of satisfying the classical ordering condition as well as monotonicity. Under technical conditions that are natural in an Anscombe-Aumann environment, we show that even for such general preference model it is possible to identify a set of priors, as first envisioned by Ellsberg (1961). We then discuss ambiguity attitudes, as well as unambiguous acts and events, for the class of rational preferences we consider.

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Bibliographic Info

Paper provided by Collegio Carlo Alberto in its series Carlo Alberto Notebooks with number 169.

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Length: 42 pages
Date of creation: 2010
Date of revision:
Handle: RePEc:cca:wpaper:169

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Keywords: Rational Preferences; Ambiguity; Unambiguous Acts and Events;

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References

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  1. Itzhak Gilboa & Fabio Maccheroni & Massimo Marinacci & David Schmeidler, 2008. "Objective and Subjective Rationality in a Multiple Prior Model," Carlo Alberto Notebooks 73, Collegio Carlo Alberto, revised 2008.
  2. Tomasz Strzalecki, . "Probabilistic Sophistication and Variational Preferences," Working Paper 8337, Harvard University OpenScholar.
  3. Ghirardato, Paolo & Marinacci, Massimo, 2002. "Ambiguity Made Precise: A Comparative Foundation," Journal of Economic Theory, Elsevier, vol. 102(2), pages 251-289, February.
  4. Machina, Mark J & Schmeidler, David, 1992. "A More Robust Definition of Subjective Probability," Econometrica, Econometric Society, vol. 60(4), pages 745-80, July.
  5. David Schmeidler, 1989. "Subjective Probability and Expected Utility without Additivity," Levine's Working Paper Archive 7662, David K. Levine.
  6. Epstein, L.G. & Zhang, J., 1998. "Subjective Probabilities on Subjectivity Unambiguous Event," RCER Working Papers 456, University of Rochester - Center for Economic Research (RCER).
  7. Cerreia-Vioglio, S. & Maccheroni, F. & Marinacci, M. & Montrucchio, L., 2011. "Uncertainty averse preferences," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1275-1330, July.
  8. Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo, 2004. "Differentiating ambiguity and ambiguity attitude," Journal of Economic Theory, Elsevier, vol. 118(2), pages 133-173, October.
  9. Paolo Ghirardato & Fabio Maccheroni & Massimo Marinacci, 2002. "Certainty Independence and the Separation of Utility and Beliefs," ICER Working Papers - Applied Mathematics Series 40-2002, ICER - International Centre for Economic Research.
  10. Klaus Nehring, 2006. "Bernoulli Without Bayes: A Theory of Utility-Sophisticated Preferences under Ambiguity," Economics Working Papers 0072, Institute for Advanced Study, School of Social Science.
  11. Paolo Ghirardato & Marciano Siniscalchi, 2010. "A more robust definition of multiple priors," Carlo Alberto Notebooks 144, Collegio Carlo Alberto.
  12. Paolo Ghirardato & Massimo Marinacci, 2000. "Risk, Ambiguity, and the Separation of Utility and Beliefs," Levine's Working Paper Archive 7616, David K. Levine.
  13. Marciano Siniscalchi, 2007. "Vector Expected Utility and Attitudes toward Variation," Discussion Papers 1455, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  14. Nehring, Klaus, 1999. "Capacities and probabilistic beliefs: a precarious coexistence," Mathematical Social Sciences, Elsevier, vol. 38(2), pages 197-213, September.
  15. 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.
  16. Massimo Marinacci, 2001. "Probabilistic sophistication and multiple priors," ICER Working Papers - Applied Mathematics Series 08-2001, ICER - International Centre for Economic Research.
  17. Nehring, Klaus, 2009. "Imprecise probabilistic beliefs as a context for decision-making under ambiguity," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1054-1091, May.
  18. Kopylov, Igor, 2007. "Subjective probabilities on "small" domains," Journal of Economic Theory, Elsevier, vol. 133(1), pages 236-265, March.
  19. Epstein, Larry G & Zhang, Jiankang, 2001. "Subjective Probabilities on Subjectively Unambiguous Events," Econometrica, Econometric Society, vol. 69(2), pages 265-306, March.
  20. Sujoy Mukerji & Peter Klibanoff, 2002. "A Smooth Model of Decision,Making Under Ambiguity," Economics Series Working Papers 113, University of Oxford, Department of Economics.
  21. Aurelien Baillon & Olivier L'Haridon & Laetitia Placido, 2011. "Ambiguity Models and the Machina Paradoxes," American Economic Review, American Economic Association, vol. 101(4), pages 1547-60, June.
  22. 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.
  23. Amarante, Massimiliano & Filiz, Emel, 2007. "Ambiguous events and maxmin expected utility," Journal of Economic Theory, Elsevier, vol. 134(1), pages 1-33, May.
  24. Epstein, Larry G, 1999. "A Definition of Uncertainty Aversion," Review of Economic Studies, Wiley Blackwell, vol. 66(3), pages 579-608, July.
  25. 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.
  26. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
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