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Perceived Ambiguity and Relevant Measures

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  • Sujoy Mukerji
  • Peter Klibanoff
  • Kyoungwon Seo

Abstract

We axiomatize preferences that can be represented by a monotonic aggregation of subjective expected utilities generated by a utility function and some set of i.i.d. probability measures over a product state space, S1. For such preferences, we define relevant measures, show that they are treated as if they were the only marginals possibly governing the state space and connect them with the measures appearing in the aforementioned representation. These results allow us to interpret relevant measures as reflecting part of perceived ambiguity, meaning subjective uncertainty about probabilities over states. Under mild conditions, we show that increases or decreases in ambiguity aversion cannot affect the relevant measures. This property, necessary for the conclusion that these measures reflect only perceived ambiguity, distinguishes the set of relevant measures from the leading alternative in the literature. We apply our findings to a number of well-known models of ambiguity-sensitive preferences. For each model, we identify the set of relevant measures and the implications of comparative ambiguity aversion.

Suggested Citation

  • Sujoy Mukerji & Peter Klibanoff & Kyoungwon Seo, 2014. "Perceived Ambiguity and Relevant Measures," Economics Series Working Papers 711, University of Oxford, Department of Economics.
  • Handle: RePEc:oxf:wpaper:711
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    Cited by:

    1. Filiz-Ozbay, Emel & Gulen, Huseyin & Masatlioglu, Yusufcan & Ozbay, Erkut Y., 2022. "Comparing ambiguous urns with different sizes," Journal of Economic Theory, Elsevier, vol. 199(C).
    2. Madhav Chandrasekher & Mira Frick & Ryota Iijima & Yves Le Yaouanq, 2022. "Dual‐Self Representations of Ambiguity Preferences," Econometrica, Econometric Society, vol. 90(3), pages 1029-1061, May.
    3. Eric Danan & Thibault Gajdos & Brian Hill & Jean-Marc Tallon, 2016. "Robust Social Decisions," American Economic Review, American Economic Association, vol. 106(9), pages 2407-2425, September.
    4. Larry G Epstein & Yoram Halevy, 2019. "Ambiguous Correlation," Review of Economic Studies, Oxford University Press, vol. 86(2), pages 668-693.
    5. Jewitt, Ian & Mukerji, Sujoy, 2017. "Ordering ambiguous acts," Journal of Economic Theory, Elsevier, vol. 171(C), pages 213-267.
    6. Ellis, Andrew, 2018. "On dynamic consistency in ambiguous games," Games and Economic Behavior, Elsevier, vol. 111(C), pages 241-249.
    7. Hill, Brian, 2023. "Beyond uncertainty aversion," Games and Economic Behavior, Elsevier, vol. 141(C), pages 196-222.
    8. Gul, Faruk & Pesendorfer, Wolfgang, 2020. "Calibrated uncertainty," Journal of Economic Theory, Elsevier, vol. 188(C).
    9. Hill , Brian & Danan , Eric, 2014. "Aggregating Tastes, Beliefs, and Attitudes Under Uncertainty," HEC Research Papers Series 1057, HEC Paris.
    10. Mira Frick & Ryota Iijima & Yves Le Yaouanq, 2019. "Dispersed Behavior and Perceptions in Assortative Societies," Cowles Foundation Discussion Papers 2180, Cowles Foundation for Research in Economics, Yale University.
    11. Bose, Subir & Daripa, Arup, 2022. "Eliciting ambiguous beliefs using constructed ambiguous acts: Alpha-maxmin," Journal of Mathematical Economics, Elsevier, vol. 103(C).
    12. Patrick Schmidt, 2019. "Eliciting ambiguity with mixing bets," Papers 1902.07447, arXiv.org, revised Jul 2022.
    13. Epstein, Larry G. & Seo, Kyoungwon, 2015. "Exchangeable capacities, parameters and incomplete theories," Journal of Economic Theory, Elsevier, vol. 157(C), pages 879-917.
    14. Klibanoff, Peter & Mukerji, Sujoy & Seo, Kyoungwon & Stanca, Lorenzo, 2022. "Foundations of ambiguity models under symmetry: α-MEU and smooth ambiguity," Journal of Economic Theory, Elsevier, vol. 199(C).
    15. Frick, Mira & Iijima, Ryota & Le Yaouanq, Yves, 2019. "Boolean Representations of Preferences under Ambiguity," Rationality and Competition Discussion Paper Series 173, CRC TRR 190 Rationality and Competition.
    16. Roee Teper, 2016. "Who is a Bayesian?," Working Paper 5861, Department of Economics, University of Pittsburgh.
    17. Peter Klibanoff & Sujoy Mukerji & Kyoungwon Seo & Lorenzo Staca, 2021. "Foundations of ambiguity models under symmetry: α-MEU and smooth ambiguity," Working Papers 922, Queen Mary University of London, School of Economics and Finance.
    18. Brian Hill, 2023. "Beyond Uncertainty Aversion," Post-Print hal-02428398, HAL.
    19. Claudia Ravanelli & Gregor Svindland, 2019. "Ambiguity sensitive preferences in Ellsberg frameworks," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 67(1), pages 53-89, February.
    20. Ghirardato, Paolo & Pennesi, Daniele, 2020. "A general theory of subjective mixtures," Journal of Economic Theory, Elsevier, vol. 188(C).

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    More about this item

    Keywords

    Symmetry; beliefs; ambiguity; ambiguity aversion; sets of probabilities;
    All these keywords.

    JEL classification:

    • D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles
    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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