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A Simple Axiomatization of Iterated Choquet Objectives

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  • Kiyohiko G. Nishimura

    (Faculty of Economics, The University of Tokyo)

  • Hiroyuki Ozaki

    (Faculty of Economics, Tohoku University)

Abstract

A set of axioms which characterizes a preference representable by the iterated Choquet expected utility is presented. This objective function is attractive since it possesses a feature of dynamical consistency. Furthermore,we show that under the same axioms the conditional preference is represented by the Choquet expected utility with respect to the capacity which is updated according to the Dempster-Shafer rule. We do this by weakening Schmeidler's axiom of comonotonic independence to our axiom of constrained comonotonic independence and by adding the axiom of dynamical consistency.

Suggested Citation

  • Kiyohiko G. Nishimura & Hiroyuki Ozaki, 2003. "A Simple Axiomatization of Iterated Choquet Objectives," CIRJE F-Series CIRJE-F-219, CIRJE, Faculty of Economics, University of Tokyo.
  • Handle: RePEc:tky:fseres:2003cf219
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    File URL: http://www.cirje.e.u-tokyo.ac.jp/research/dp/2003/2003cf219.pdf
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    References listed on IDEAS

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    1. Gilboa Itzhak & Schmeidler David, 1993. "Updating Ambiguous Beliefs," Journal of Economic Theory, Elsevier, vol. 59(1), pages 33-49, February.
    2. Paolo Ghirardato, 2002. "Revisiting Savage in a conditional world," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 20(1), pages 83-92.
    3. Yoo, Keuk-Ryoul, 1991. "The iterative law of expectation and non-additive probability measure," Economics Letters, Elsevier, vol. 37(2), pages 145-149, October.
    4. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
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    Cited by:

    1. Klibanoff, Peter & Marinacci, Massimo & Mukerji, Sujoy, 2009. "Recursive smooth ambiguity preferences," Journal of Economic Theory, Elsevier, vol. 144(3), pages 930-976, May.
    2. Kast, Robert & Lapied, André & Roubaud, David, 2014. "Modelling under ambiguity with dynamically consistent Choquet random walks and Choquet–Brownian motions," Economic Modelling, Elsevier, vol. 38(C), pages 495-503.
    3. Hanany Eran & Klibanoff Peter, 2009. "Updating Ambiguity Averse Preferences," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 9(1), pages 1-53, November.
    4. André Lapied & Pascal Tocquebeuf, 2007. "Consistent Dynamice Choice And Non-Expected Utility Preferences," Working Papers halshs-00353880, HAL.

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