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Unambiguous events and dynamic Choquet preferences

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  • Adam Dominiak
  • Jean-Philippe Lefort

Abstract

This paper explores the relationship between dynamic consistency and the existing notions of unambiguous events for Choquet expected utility preferences. A decision maker is faced with an information structure represented by a filtration. We show that the decision maker's preferences respect dynamic consistency on a fixed filtration if and only if the last stage of the filtration is composed of unambiguous events in the sense of Nehring (1999). Adopting two axioms, conditional certainty equivalence consistency and constrained dynamic consistency to filtration measurable acts, it is shown that the decision maker respects these two axioms on a fixed filtration if and only if the last stage of the filtration is made up of unambiguous events the sense of Zhang (2002).
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  • Adam Dominiak & Jean-Philippe Lefort, 2011. "Unambiguous events and dynamic Choquet preferences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 46(3), pages 401-425, April.
    • Handle: RePEc:spr:joecth:v:46:y:2011:i:3:p:401-425
    DOI: 10.1007/s00199-009-0512-7
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    Cited by:

    1. Jürgen Eichberger & Simon Grant & David Kelsey, 2012. "When is ambiguity–attitude constant?," Journal of Risk and Uncertainty, Springer, vol. 45(3), pages 239-263, December.
    2. André Lapied & Pascal Toquebeuf, 2011. "Dynamically consistent CEU preferences," Working Papers halshs-00856193, HAL.
    3. Takao Asano & Hiroyuki Kojima, 2019. "Consequentialism and dynamic consistency in updating ambiguous beliefs," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 68(1), pages 223-250, July.
    4. Spyros Galanis, 2021. "Dynamic consistency, valuable information and subjective beliefs," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(4), pages 1467-1497, June.
    5. Billot, Antoine & Vergopoulos, Vassili, 2018. "Expected utility without parsimony," Mathematical Social Sciences, Elsevier, vol. 93(C), pages 14-21.
    6. André Lapied & Pascal Tocquebeuf, 2007. "Consistent Dynamice Choice And Non-Expected Utility Preferences," Working Papers halshs-00353880, HAL.
    7. Massimiliano Amarante, 2017. "Conditional expected utility," Theory and Decision, Springer, vol. 83(2), pages 175-193, August.
    8. repec:dau:papers:123456789/8575 is not listed on IDEAS
    9. Nobuo Koida, 2012. "Nest-monotonic two-stage acts and exponential probability capacities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 50(1), pages 99-124, May.
    10. Dominiak, Adam & Lee, Min Suk, 2017. "Coherent Dempster–Shafer equilibrium and ambiguous signals," Journal of Mathematical Economics, Elsevier, vol. 68(C), pages 42-54.
    11. Matthew Kovach, 2021. "Ambiguity and Partial Bayesian Updating," Papers 2102.11429, arXiv.org, revised Mar 2023.
    12. 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.
    13. Lapied, André & Toquebeuf, Pascal, 2012. "Dynamically consistent CEU preferences on f-convex events," Mathematical Social Sciences, Elsevier, vol. 63(3), pages 252-256.
    14. Takao Asano & Hiroyuki Kojima, 2018. "Consequentialism and Dynamic Consistency in Updating Ambiguous Beliefs," KIER Working Papers 987, Kyoto University, Institute of Economic Research.
    15. Dominiak, Adam, 2013. "Iterated Choquet expectations: A possibility result," Economics Letters, Elsevier, vol. 120(2), pages 155-159.
    16. Adam Dominiak & Ani Guerdjikova, 2021. "Pessimism and optimism towards new discoveries," Theory and Decision, Springer, vol. 90(3), pages 321-370, May.
    17. Dominiak, Adam & Lefort, Jean-Philippe, 2015. "“Agreeing to disagree” type results under ambiguity," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 119-129.
    18. Stefan Trautmann & Peter P. Wakker, 2018. "Making the Anscombe-Aumann approach to ambiguity suitable for descriptive applications," Journal of Risk and Uncertainty, Springer, vol. 56(1), pages 83-116, February.

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    More about this item

    Keywords

    Choquet expected utility; Unambiguous events; Filtration; Updating; Dynamic consistency; Consequentialism; D81; D82;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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