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Unbounded probabilistic sophistication

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  • Kopylov, Igor

Abstract

I extend Machina and Schmeidler's (1992) model of probabilistic sophistication to unbounded uncertain prospects (acts) and derive risk preferences over the induced probability distributions (lotteries) with unbounded support. For example, risk preferences can be derived over normal, exponential, and Poisson families of probability distributions. My extension uses a version of Arrow's (1970) Monotone Continuity, which implies countable additivity for subjective beliefs and a novel property of tail-continuity for the revealed risk preferences. On the other hand, I do not assume P6 (Small Event Continuity) that is used both by Savage (1954) and Machina-Schmeidler.

Suggested Citation

  • Kopylov, Igor, 2010. "Unbounded probabilistic sophistication," Mathematical Social Sciences, Elsevier, vol. 60(2), pages 113-118, September.
    • Handle: RePEc:eee:matsoc:v:60:y:2010:i:2:p:113-118
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    References listed on IDEAS

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    1. Sarin, Rakesh & Wakker, Peter P., 2000. "Cumulative dominance and probabilistic sophistication," Mathematical Social Sciences, Elsevier, vol. 40(2), pages 191-196, September.
    2. Alain Chateauneuf & Fabio Maccheroni & Massimo Marinacci & Jean-Marc Tallon, 2005. "Monotone continuous multiple priors," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(4), pages 973-982, November.
    3. Massimo Marinacci, 2002. "Probabilistic Sophistication and Multiple Priors," Econometrica, Econometric Society, vol. 70(2), pages 755-764, March.
    4. Machina, Mark J & Schmeidler, David, 1992. "A More Robust Definition of Subjective Probability," Econometrica, Econometric Society, vol. 60(4), pages 745-780, July.
    5. Kopylov, Igor, 2010. "Simple axioms for countably additive subjective probability," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 867-876, September.
    6. Peter Wakker, 1993. "Savage's Axioms Usually Imply Violation of Strict Stochastic Dominance," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 60(2), pages 487-493.
    7. 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.
    8. 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.
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    1. Kopylov, Igor, 2016. "Canonical utility functions and continuous preference extensions," Journal of Mathematical Economics, Elsevier, vol. 67(C), pages 32-37.
    2. Amit Kothiyal & Vitalie Spinu & Peter P. Wakker, 2014. "Average Utility Maximization: A Preference Foundation," Operations Research, INFORMS, vol. 62(1), pages 207-218, February.

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