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Ordering ambiguous acts

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  • Jewitt, Ian
  • Mukerji, Sujoy

Abstract

We investigate what it means for one act to be more ambiguous than another. The question is evidently analogous to asking what makes one prospect riskier than another, but beliefs are neither objective nor representable by a unique probability. Our starting point is an abstract class of preferences constructed to be (strictly) partially ordered by a more ambiguity averse relation. First, we define two notions of more ambiguous with respect to such a class. A more ambiguous (I) act makes an ambiguity averse decision maker (DM) worse off but does not affect the welfare of an ambiguity neutral DM. A more ambiguous (II) act adversely affects a more ambiguity averse DM more, as measured by the compensation they require to switch acts. Unlike more ambiguous (I), more ambiguous (II) does not require indifference of ambiguity neutral elements to the acts being compared. Second, we implement the abstract definitions to characterize more ambiguous (I) and (II) for two explicit preference families: α-maxmin expected utility and smooth ambiguity. Thirdly, we give applications to the comparative statics of more ambiguous in a standard portfolio problem and a consumption-saving problem.

Suggested Citation

  • Jewitt, Ian & Mukerji, Sujoy, 2017. "Ordering ambiguous acts," Journal of Economic Theory, Elsevier, vol. 171(C), pages 213-267.
  • Handle: RePEc:eee:jetheo:v:171:y:2017:i:c:p:213-267
    DOI: 10.1016/j.jet.2017.07.001
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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. Miao, Jianjun & Wang, Neng, 2011. "Risk, uncertainty, and option exercise," Journal of Economic Dynamics and Control, Elsevier, vol. 35(4), pages 442-461, April.
    3. Hackbarth, Dirk & Miao, Jianjun, 2012. "The dynamics of mergers and acquisitions in oligopolistic industries," Journal of Economic Dynamics and Control, Elsevier, vol. 36(4), pages 585-609.
    4. Cherbonnier, Frédéric & Gollier, Christian, 2015. "Decreasing aversion under ambiguity," Journal of Economic Theory, Elsevier, vol. 157(C), pages 606-623.
    5. Kellner, Christian, 2015. "Tournaments as a response to ambiguity aversion in incentive contracts," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 627-655.
    6. Aflaki, Sam, 2013. "The effect of environmental uncertainty on the tragedy of the commons," Games and Economic Behavior, Elsevier, vol. 82(C), pages 240-253.
    7. repec:eee:wdevel:v:100:y:2017:i:c:p:69-84 is not listed on IDEAS
    8. Fujii, Tomoki, 2017. "Dynamic Poverty Decomposition Analysis: An Application to the Philippines," World Development, Elsevier, vol. 100(C), pages 69-84.
    9. Loïc Berger, 2011. "Smooth Ambiguity Aversion in the Small and in the Large," Working Papers ECARES ECARES 2011-020, ULB -- Universite Libre de Bruxelles.
    10. L. A. Franzoni, 2016. "Optimal liability design under risk and ambiguity," Working Papers wp1048, Dipartimento Scienze Economiche, Universita' di Bologna.
    11. Ruffino, Doriana, 2013. "A Robust Capital Asset Pricing Model," Finance and Economics Discussion Series 2014-1, Board of Governors of the Federal Reserve System (U.S.).
    12. Yehuda Izhakian, 2012. "Ambiguity Measurement," Working Papers 12-01, New York University, Leonard N. Stern School of Business, Department of Economics.
    13. Alan Rogers & Matthew Ryan, 2012. "Additivity and Uncertainty," Economics Bulletin, AccessEcon, vol. 32(3), pages 1858-1864.
    14. Izhakian, Yehuda, 2017. "Expected utility with uncertain probabilities theory," Journal of Mathematical Economics, Elsevier, vol. 69(C), pages 91-103.

    More about this item

    Keywords

    Ambiguity; Knightian uncertainty; Ambiguity aversion; Comparative statics; Single-crossing; More ambiguous;

    JEL classification:

    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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