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Evaluating Ambiguous Random Variables and Updating by Proxy

Author

Listed:
  • Faruk Gul

    (Princeton University)

  • Wolfgang Pesendorfer

    (Princeton University)

Abstract

We introduce a new theory of belief revision under ambiguity. It is recursive (random variables are evaluated by backward induction) and consequentialist (the conditional expectation of any random variable depends only on the values the random variable attains on the conditioning event). Agents experience no change in preferences but may not be indifferent to the timing of resolution of uncertainty. We provide three main theorems: the first relates our rule to standard Bayesian updating; the others characterize the dynamic behavior of an agent who adopts our rule.

Suggested Citation

  • Faruk Gul & Wolfgang Pesendorfer, 2018. "Evaluating Ambiguous Random Variables and Updating by Proxy," Working Papers 2018-7, Princeton University. Economics Department..
    • Handle: RePEc:pri:econom:2018-7
    as

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    File URL: http://www.princeton.edu/~pesendor/Updating.pdf
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    References listed on IDEAS

    as
    1. Paolo Ghirardato & Massimo Marinacci, 2001. "Risk, Ambiguity, and the Separation of Utility and Beliefs," Mathematics of Operations Research, INFORMS, vol. 26(4), pages 864-890, November.
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    7. Itzhak Gilboa & David Schmeidler, 1992. "Additive Representation of Non-Additive Measures and the Choquet Integral," Discussion Papers 985, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    8. ,, 2011. "Dynamic choice under ambiguity," Theoretical Economics, Econometric Society, vol. 6(3), September.
    9. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    10. Daniel Ellsberg, 1961. "Risk, Ambiguity, and the Savage Axioms," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 75(4), pages 643-669.
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    12. 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. Lorenzo Bastianello & José Heleno Faro, 2023. "Choquet expected discounted utility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 75(4), pages 1071-1098, May.

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    More about this item

    Keywords

    Radom Variables; Ambiguity;

    JEL classification:

    • D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles

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