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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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    1. Gajdos, Thibault & Tallon, Jean-Marc & Vergnaud, Jean-Christophe, 2004. "Decision making with imprecise probabilistic information," Journal of Mathematical Economics, Elsevier, vol. 40(6), pages 647-681, September.
    2. Cerreia-Vioglio, S. & Maccheroni, F. & Marinacci, M. & Montrucchio, L., 2011. "Uncertainty averse preferences," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1275-1330, July.
    3. Tapking, Jens, 2004. "Axioms for preferences revealing subjective uncertainty and uncertainty aversion," Journal of Mathematical Economics, Elsevier, vol. 40(7), pages 771-797, November.
    4. Gajdos, T. & Hayashi, T. & Tallon, J.-M. & Vergnaud, J.-C., 2008. "Attitude toward imprecise information," Journal of Economic Theory, Elsevier, vol. 140(1), pages 27-65, May.
    5. Robert F. Nau, 2006. "Uncertainty Aversion with Second-Order Utilities and Probabilities," Management Science, INFORMS, vol. 52(1), pages 136-145, January.
    6. Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo, 2004. "Differentiating ambiguity and ambiguity attitude," Journal of Economic Theory, Elsevier, vol. 118(2), pages 133-173, October.
    7. Epstein Larry G & Seo Kyoungwon, 2011. "Symmetry or Dynamic Consistency?," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 11(1), pages 1-14, June.
    8. Siniscalchi, Marciano, 2006. "A behavioral characterization of plausible priors," Journal of Economic Theory, Elsevier, vol. 128(1), pages 91-135, May.
    9. Dekel, Eddie & Lipman, Barton L & Rustichini, Aldo, 2001. "Representing Preferences with a Unique Subjective State Space," Econometrica, Econometric Society, vol. 69(4), pages 891-934, July.
    10. Kyoungwon Seo, 2009. "Ambiguity and Second-Order Belief," Econometrica, Econometric Society, vol. 77(5), pages 1575-1605, September.
    11. Itzhak Gilboa & Fabio Maccheroni & Massimo Marinacci & David Schmeidler, 2010. "Objective and Subjective Rationality in a Multiple Prior Model," Econometrica, Econometric Society, vol. 78(2), pages 755-770, March.
    12. Paolo Ghirardato & Marciano Siniscalchi, 2012. "Ambiguity in the Small and in the Large," Econometrica, Econometric Society, vol. 80(6), pages 2827-2847, November.
    13. Cerreia-Vioglio, Simone & Maccheroni, Fabio & Marinacci, Massimo & Montrucchio, Luigi, 2013. "Ambiguity and robust statistics," Journal of Economic Theory, Elsevier, vol. 148(3), pages 974-1049.
      • Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci & Luigi Montrucchio, 2011. "Ambiguity and Robust Statistics," Working Papers 382, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    14. Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini, 2006. "Ambiguity Aversion, Robustness, and the Variational Representation of Preferences," Econometrica, Econometric Society, vol. 74(6), pages 1447-1498, November.
    15. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    16. Peter Klibanoff & Massimo Marinacci & Sujoy Mukerji, 2005. "A Smooth Model of Decision Making under Ambiguity," Econometrica, Econometric Society, vol. 73(6), pages 1849-1892, November.
    17. Marciano Siniscalchi, 2009. "Vector Expected Utility and Attitudes Toward Variation," Econometrica, Econometric Society, vol. 77(3), pages 801-855, May.
    18. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    19. Simone Cerreia-Vioglio & Paolo Ghirardato & Fabio Maccheroni & Massimo Marinacci & Marciano Siniscalchi, 2011. "Rational preferences under ambiguity," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(2), pages 341-375, October.
    20. Amarante, Massimiliano, 2009. "Foundations of neo-Bayesian statistics," Journal of Economic Theory, Elsevier, vol. 144(5), pages 2146-2173, September.
    21. Ghirardato, Paolo & Marinacci, Massimo, 2002. "Ambiguity Made Precise: A Comparative Foundation," Journal of Economic Theory, Elsevier, vol. 102(2), pages 251-289, February.
    22. Al-Najjar, Nabil I. & De Castro, Luciano, 2014. "Parametric representation of preferences," Journal of Economic Theory, Elsevier, vol. 150(C), pages 642-667.
    23. David S. Ahn, 2008. "Ambiguity Without a State Space," Review of Economic Studies, Oxford University Press, vol. 75(1), pages 3-28.
    24. Epstein, Larry G. & Seo, Kyoungwon, 2010. "Symmetry of evidence without evidence of symmetry," Theoretical Economics, Econometric Society, vol. 5(3), September.
    25. Yaari, Menahem E., 1969. "Some remarks on measures of risk aversion and on their uses," Journal of Economic Theory, Elsevier, vol. 1(3), pages 315-329, October.
    26. Larry G. Epstein, 1999. "A Definition of Uncertainty Aversion," Review of Economic Studies, Oxford University Press, vol. 66(3), pages 579-608.
    27. Daniel Ellsberg, 1961. "Risk, Ambiguity, and the Savage Axioms," The Quarterly Journal of Economics, Oxford University Press, vol. 75(4), pages 643-669.
    28. Wojciech Olszewski, 2007. "Preferences Over Sets of Lotteries -super-1," Review of Economic Studies, Oxford University Press, vol. 74(2), pages 567-595.
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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. 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.
    3. Larry G Epstein & Yoram Halevy, 2019. "Ambiguous Correlation," Review of Economic Studies, Oxford University Press, vol. 86(2), pages 668-693.
    4. Ellis, Andrew, 2018. "On dynamic consistency in ambiguous games," Games and Economic Behavior, Elsevier, vol. 111(C), pages 241-249.
    5. Jewitt, Ian & Mukerji, Sujoy, 2017. "Ordering ambiguous acts," Journal of Economic Theory, Elsevier, vol. 171(C), pages 213-267.
    6. Epstein, Larry G. & Seo, Kyoungwon, 2015. "Exchangeable capacities, parameters and incomplete theories," Journal of Economic Theory, Elsevier, vol. 157(C), pages 879-917.
    7. Roee Teper, 2016. "Who is a Bayesian?," Working Paper 5861, Department of Economics, University of Pittsburgh.
    8. 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.
    9. Gul, Faruk & Pesendorfer, Wolfgang, 2020. "Calibrated uncertainty," Journal of Economic Theory, Elsevier, vol. 188(C).
    10. Patrick Schmidt, 2019. "Elicitation of ambiguous beliefs with mixing bets," Papers 1902.07447, arXiv.org, revised Oct 2021.
    11. 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).
    12. 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.
    13. 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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