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Updating Ambiguity Averse Preferences

Author

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  • Hanany Eran

    () (Tel Aviv University)

  • Klibanoff Peter

    () (Northwestern University)

Abstract

Dynamic consistency leads to Bayesian updating under expected utility. We ask what it implies for the updating of more general preferences. In this paper, we characterize dynamically consistent update rules for preference models satisfying ambiguity aversion. This characterization extends to regret-based models as well. As applications of our general result, we characterize dynamically consistent updating for two important models of ambiguity averse preferences: the ambiguity averse smooth ambiguity preferences (Klibanoff, Marinacci and Mukerji [Econometrica 73 2005, pp. 1849-1892]) and the variational preferences (Maccheroni, Marinacci and Rustichini [Econometrica 74 2006, pp. 1447-1498]). The latter includes max-min expected utility (Gilboa and Schmeidler [Journal of Mathematical Economics 18 1989, pp. 141-153]) and the multiplier preferences of Hansen and Sargent [American Economic Review 91(2) 2001, pp. 60-66] as special cases. For smooth ambiguity preferences, we also identify a simple rule that is shown to be the unique dynamically consistent rule among a large class of rules that may be expressed as reweightings of the Bayes' rule.

Suggested Citation

  • Hanany Eran & Klibanoff Peter, 2009. "Updating Ambiguity Averse Preferences," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 9(1), pages 1-53, November.
  • Handle: RePEc:bpj:bejtec:v:9:y:2009:i:1:n:37
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci, 2015. "On the equality of Clarke-Rockafellar and Greenberg-Pierskalla differentials for monotone and quasiconcave functionals," Working Papers 561, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    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. Cerreia-Vioglio, S. & Maccheroni, F. & Marinacci, M. & Rustichini, A., 2015. "The structure of variational preferences," Journal of Mathematical Economics, Elsevier, vol. 57(C), pages 12-19.
    4. Kellner, Christian & Le Quement, Mark T., 2018. "Endogenous ambiguity in cheap talk," Journal of Economic Theory, Elsevier, vol. 173(C), pages 1-17.
    5. Lang, Matthias & Wambach, Achim, 2013. "The fog of fraud – Mitigating fraud by strategic ambiguity," Games and Economic Behavior, Elsevier, vol. 81(C), pages 255-275.
    6. Roee Teper, 2016. "Who is a Bayesian?," Working Paper 5861, Department of Economics, University of Pittsburgh.
    7. Karni, Edi & Maccheroni, Fabio & Marinacci, Massimo, 2015. "Ambiguity and Nonexpected Utility," Handbook of Game Theory with Economic Applications, Elsevier.
    8. AMARANTE, Massimiliano, 2014. "What is ambiguity?," Cahiers de recherche 2014-01, Universite de Montreal, Departement de sciences economiques.
    9. Lapied, André & Toquebeuf, Pascal, 2012. "Dynamically consistent CEU preferences on f-convex events," Mathematical Social Sciences, Elsevier, vol. 63(3), pages 252-256.
    10. Dominiak, Adam & Lefort, Jean-Philippe, 2015. "“Agreeing to disagree” type results under ambiguity," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 119-129.
    11. repec:eee:gamebe:v:104:y:2017:i:c:p:271-292 is not listed on IDEAS
    12. Massimiliano Amarante, 2017. "Conditional expected utility," Theory and Decision, Springer, vol. 83(2), pages 175-193, August.
    13. Othon M. Moreno & Yaroslav Rosokha, 2016. "Learning under compound risk vs. learning under ambiguity – an experiment," Journal of Risk and Uncertainty, Springer, vol. 53(2), pages 137-162, December.
    14. Joseph Y. Halpern & Samantha Leung, 2016. "Minimizing regret in dynamic decision problems," Theory and Decision, Springer, vol. 81(1), pages 123-151, June.
    15. Dominiak, Adam, 2013. "Iterated Choquet expectations: A possibility result," Economics Letters, Elsevier, vol. 120(2), pages 155-159.
    16. Alexander Zimper, 2011. "Do Bayesians Learn Their Way Out of Ambiguity?," Decision Analysis, INFORMS, vol. 8(4), pages 269-285, December.
    17. Massimo Marinacci, 2015. "Model Uncertainty," Journal of the European Economic Association, European Economic Association, vol. 13(6), pages 1022-1100, December.
    18. Azrieli, Yaron & Teper, Roee, 2011. "Uncertainty aversion and equilibrium existence in games with incomplete information," Games and Economic Behavior, Elsevier, vol. 73(2), pages 310-317.
    19. Pierpaolo Battigalli & Alejandro Francetich & Giacomo Lanzani & Massimo Marinacci, 2016. "Learning and Self-confi rming Long-Run Biases," Working Papers 588, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    20. Gumen, Anna & Savochkin, Andrei, 2013. "Dynamically stable preferences," Journal of Economic Theory, Elsevier, vol. 148(4), pages 1487-1508.
    21. Pierpaolo Battigalli & Emiliano Catonini & Giacomo Lanzani & Massimo Marinacci, 2017. "Ambiguity Attitudes and Self-Confi rming Equilibrium in Sequential Games," Working Papers 607, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.

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