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Decision-Making in the Context of Imprecise Probabilistic Beliefs

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Author Info
Klaus Nehring () (Department of Economics, University of California Davis)
Abstract

Coherent imprecise probabilistic beliefs are modelled as incomplete comparative likelihood relations admitting a multiple-prior representation. Under a structural assumption of Equidivisibility, we provide an axiomatization of such relations and show uniqueness of the representation. In the second part of the paper, we formulate a behaviorally general axiom relating preferences and probabilistic beliefs which implies that preferences over unambiguous acts are probabilistically sophisticated and which entails representability of preferences over Savage acts in an Anscombe-Aumann-style framework. The motivation for an explicit and separate axiomatization of beliefs for the study of decision-making under ambiguity is discussed in some detail.

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Paper provided by Institute for Advanced Study, School of Social Science in its series Economics Working Papers with number 0034.

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Length: 52 pages
Date of creation: Apr 2006
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Handle: RePEc:ads:wpaper:0034

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  1. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April. [Downloadable!] (restricted)
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  3. Peter Klibanoff, 2001. "Characterizing uncertainty aversion through preference for mixtures," Social Choice and Welfare, Springer, vol. 18(2), pages 289-301. [Downloadable!] (restricted)
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  8. Sarin, Rakesh & Wakker, Peter P., 2000. "Cumulative dominance and probabilistic sophistication," Mathematical Social Sciences, Elsevier, vol. 40(2), pages 191-196, September. [Downloadable!] (restricted)
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  12. Nehring, Klaus, 1999. "Capacities and probabilistic beliefs: a precarious coexistence," Mathematical Social Sciences, Elsevier, vol. 38(2), pages 197-213, September. [Downloadable!] (restricted)
  13. Epstein, Larry G & Zhang, Jiankang, 2001. "Subjective Probabilities on Subjectively Unambiguous Events," Econometrica, Econometric Society, vol. 69(2), pages 265-306, March.
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  14. Kopylov, Igor, 2007. "Subjective probabilities on "small" domains," Journal of Economic Theory, Elsevier, vol. 133(1), pages 236-265, March. [Downloadable!] (restricted)
  15. Massimo Marinacci, 2002. "Probabilistic Sophistication and Multiple Priors," Econometrica, Econometric Society, vol. 70(2), pages 755-764, March. [Downloadable!] (restricted)
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  16. Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo, 2005. "Certainty Independence and the Separation of Utility and Beliefs," Journal of Economic Theory, Elsevier, vol. 120(1), pages 129-136, January. [Downloadable!] (restricted)
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  17. Grant, Simon, 1995. "Subjective Probability without Monotonicity: Or How Machina's Mom May Also Be Probabilistically Sophisticated," Econometrica, Econometric Society, vol. 63(1), pages 159-89, January. [Downloadable!] (restricted)
  18. Epstein, Larry G, 1999. "A Definition of Uncertainty Aversion," Review of Economic Studies, Blackwell Publishing, vol. 66(3), pages 579-608, July. [Downloadable!] (restricted)
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  20. Peter Klibanoff & Massimo Marinacci & Sujoy Mukerji, 2005. "A Smooth Model of Decision Making under Ambiguity," Econometrica, Econometric Society, vol. 73(6), pages 1849-1892, November. [Downloadable!] (restricted)
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  21. Itzhak Gilboa & Dov Samet & David Schmeidler, 2004. "Utilitarian Aggregation of Beliefs and Tastes," Journal of Political Economy, University of Chicago Press, vol. 112(4), pages 932-938, August.
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  22. Haluk Ergin & Faruk Gul, 2004. "A subjective theory of compound lotteries," Econometric Society 2004 North American Summer Meetings 152, Econometric Society. [Downloadable!]
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  23. Blume, Lawrence & Brandenburger, Adam & Dekel, Eddie, 1991. "Lexicographic Probabilities and Choice under Uncertainty," Econometrica, Econometric Society, vol. 59(1), pages 61-79, January. [Downloadable!] (restricted)
  24. Grant, Simon & Karni, Edi, 2004. "A theory of quantifiable beliefs," Journal of Mathematical Economics, Elsevier, vol. 40(5), pages 515-546, August. [Downloadable!] (restricted)
  25. Casadesus-Masanell, Ramon & Klibanoff, Peter & Ozdenoren, Emre, 2000. "Maxmin Expected Utility over Savage Acts with a Set of Priors," Journal of Economic Theory, Elsevier, vol. 92(1), pages 35-65, May. [Downloadable!] (restricted)
  26. Truman F. Bewley, 1986. "Knightian Decision Theory: Part 1," Cowles Foundation Discussion Papers 807, Cowles Foundation, Yale University. [Downloadable!]
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. 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. [Downloadable!]
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