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Probabilistic sophistication and variational preferences

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  • Tomasz, Strzalecki

Abstract

This paper shows that in the class of variational preferences the notion of probabilistic sophistication is equivalent to expected utility as long as there exists at least one event such that the independence axiom holds for bets on that event. This extends the result of Marinacci (2002) [13] and provides a novel interpretation of his result.

Suggested Citation

  • Tomasz, Strzalecki, 2011. "Probabilistic sophistication and variational preferences," Journal of Economic Theory, Elsevier, vol. 146(5), pages 2117-2125, September.
  • Handle: RePEc:eee:jetheo:v:146:y:2011:i:5:p:2117-2125
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    References listed on IDEAS

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    1. Cerreia-Vioglio, Simone & Maccheroni, Fabio & Marinacci, Massimo & Montrucchio, Luigi, 2012. "Probabilistic sophistication, second order stochastic dominance and uncertainty aversion," Journal of Mathematical Economics, Elsevier, pages 271-283.
    2. 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.
    3. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    4. Thomas J. Sargent & LarsPeter Hansen, 2001. "Robust Control and Model Uncertainty," American Economic Review, American Economic Association, vol. 91(2), pages 60-66, May.
    5. 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.
    6. Sarin, Rakesh & Wakker, Peter P., 2000. "Cumulative dominance and probabilistic sophistication," Mathematical Social Sciences, Elsevier, vol. 40(2), pages 191-196, September.
    7. Daniel Ellsberg, 2000. "Risk, Ambiguity and the Savage Axioms," Levine's Working Paper Archive 7605, David K. Levine.
    8. Simon Grant & Atsushi Kajii, 2005. "Probabilistically Sophisticated Multiple Priors," KIER Working Papers 608, Kyoto University, Institute of Economic Research.
    9. Chew Soo Hong & Jacob S. Sagi, 2006. "Event Exchangeability: Probabilistic Sophistication Without Continuity or Monotonicity," Econometrica, Econometric Society, vol. 74(3), pages 771-786, May.
    10. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    11. Grant, Simon, 1995. "Subjective Probability without Monotonicity: Or How Machina's Mom May Also Be Probabilistically Sophisticated," Econometrica, Econometric Society, vol. 63(1), pages 159-189, January.
    12. Massimo Marinacci, 2002. "Probabilistic Sophistication and Multiple Priors," Econometrica, Econometric Society, vol. 70(2), pages 755-764, March.
    13. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    14. Machina, Mark J & Schmeidler, David, 1992. "A More Robust Definition of Subjective Probability," Econometrica, Econometric Society, vol. 60(4), pages 745-780, July.
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    Cited by:

    1. Cerreia-Vioglio, Simone & Maccheroni, Fabio & Marinacci, Massimo & Montrucchio, Luigi, 2012. "Probabilistic sophistication, second order stochastic dominance and uncertainty aversion," Journal of Mathematical Economics, Elsevier, vol. 48(5), pages 271-283.
    2. Werner, Jan, 2011. "Risk aversion for variational and multiple-prior preferences," Journal of Mathematical Economics, Elsevier, vol. 47(3), pages 382-390.
    3. 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), pages 341-375.
    4. Knispel, Thomas & Laeven, Roger J.A. & Svindland, Gregor, 2016. "Robust optimal risk sharing and risk premia in expanding pools," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 182-195.
    5. Claudia Ravanelli & Gregor Svindland, 2014. "Comonotone Pareto optimal allocations for law invariant robust utilities on L 1," Finance and Stochastics, Springer, vol. 18(1), pages 249-269, January.
    6. Sergio Almeida & Marcos Rangel, 2016. "Probabilistic Sophistication, Sources Of Uncertainty, And Cognitive Ability: Experimental Evidence," Anais do XLII Encontro Nacional de Economia [Proceedings of the 42ndd Brazilian Economics Meeting] 131, ANPEC - Associação Nacional dos Centros de Pósgraduação em Economia [Brazilian Association of Graduate Programs in Economics].

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