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When is ambiguity–attitude constant?

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  • Jürgen Eichberger
  • Simon Grant
  • David Kelsey

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Abstract

This paper studies how updating affects ambiguity attitude. In particular we focus on generalized Bayesian updating of the Jaffray–Philippe sub-class of Choquet Expected Utility preferences. We find conditions for ambiguity attitude to be the same before and after updating. A necessary and sufficient condition for ambiguity attitude to be unchanged when updated on an arbitrary event is for the capacity to be neo-additive. We find a condition for updating on a given partition to preserve ambiguity attitude. We relate this to necessary and sufficient conditions for dynamic consistency. Finally, we study whether ambiguity increases or decreases after updating. Copyright Springer Science+Business Media New York 2012

Suggested Citation

  • 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.
  • Handle: RePEc:kap:jrisku:v:45:y:2012:i:3:p:239-263 DOI: 10.1007/s11166-012-9153-5
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    References listed on IDEAS

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    1. Jurgen Eichberger & Simon Grant & David Kelsey & Gleb A. Koshevoy, 2009. "The a-MEU Model: A Comment," Discussion Papers 0903, Exeter University, Department of Economics.
    2. Eichberger, Jurgen & Grant, Simon & Kelsey, David, 2007. "Updating Choquet beliefs," Journal of Mathematical Economics, Elsevier, vol. 43(7-8), pages 888-899, September.
    3. Eichberger, Jürgen & Grant, Simon & Kelsey, David & Koshevoy, Gleb A., 2011. "The [alpha]-MEU model: A comment," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1684-1698, July.
    4. Gilboa Itzhak & Schmeidler David, 1993. "Updating Ambiguous Beliefs," Journal of Economic Theory, Elsevier, vol. 59(1), pages 33-49, February.
    5. Eichberger, Jurgen & Grant, Simon & Kelsey, David, 2005. "CEU preferences and dynamic consistency," Mathematical Social Sciences, Elsevier, vol. 49(2), pages 143-151, March.
    6. Chateauneuf, Alain & Eichberger, Jurgen & Grant, Simon, 2007. "Choice under uncertainty with the best and worst in mind: Neo-additive capacities," Journal of Economic Theory, Elsevier, vol. 137(1), pages 538-567, November.
    7. Epstein, Larry G. & Schneider, Martin, 2003. "Recursive multiple-priors," Journal of Economic Theory, Elsevier, vol. 113(1), pages 1-31, November.
    8. repec:dau:papers:123456789/7323 is not listed on IDEAS
    9. Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo, 2004. "Differentiating ambiguity and ambiguity attitude," Journal of Economic Theory, Elsevier, vol. 118(2), pages 133-173, October.
    10. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    11. Eichberger, Jürgen & Grant, Simon & Kelsey, David, 2010. "Comparing three ways to update Choquet beliefs," Economics Letters, Elsevier, vol. 107(2), pages 91-94, May.
    12. 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.
    13. Sujoy Mukerji & Peter Klibanoff and Kyoungwon Seo, 2011. "Relevance and Symmetry," Economics Series Working Papers 539, University of Oxford, Department of Economics.
    14. Sarin, Rakesh & Wakker, Peter P, 1998. "Dynamic Choice and NonExpected Utility," Journal of Risk and Uncertainty, Springer, vol. 17(2), pages 87-119, November.
    15. Cohen, M. & Gilboa, I. & Jaffray, J.Y. & Schmeidler, D., 2000. "An experimental study of updating ambiguous beliefs," Risk, Decision and Policy, Cambridge University Press, vol. 5(02), pages 123-133, June.
    16. Eichberger, Jurgen & Kelsey, David, 1996. "Uncertainty Aversion and Dynamic Consistency," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 37(3), pages 625-640, August.
    17. Wakker,Peter P., 2010. "Prospect Theory," Cambridge Books, Cambridge University Press, number 9780521765015, December.
    18. Sarin, Rakesh K & Wakker, Peter, 1992. "A Simple Axiomatization of Nonadditive Expected Utility," Econometrica, Econometric Society, vol. 60(6), pages 1255-1272, November.
    19. Peter Wakker, 2011. "Jaffray’s ideas on ambiguity," Theory and Decision, Springer, vol. 71(1), pages 11-22, July.
    20. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
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    Citations

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    Cited by:

    1. Groneck, Max & Ludwig, Alexander & Zimper, Alexander, 2016. "A life-cycle model with ambiguous survival beliefs," Journal of Economic Theory, Elsevier, pages 137-180.
    2. Groneck, Max & Ludwig, Alexander & Zimper, Alexander, 2016. "A life-cycle model with ambiguous survival beliefs," Journal of Economic Theory, Elsevier, vol. 162(C), pages 137-180.
    3. : Kostas Koufopoulos & : Roman Kozhan, 2012. "Optimal Insurance under Advserse Selection and Ambiguity Aversion," Working Papers wpn12-07, Warwick Business School, Finance Group.
    4. Aurélien Baillon & Han Bleichrodt & Umut Keskin & Olivier L'Haridon & Author-Name: Chen Li, 2013. "Learning under ambiguity: An experiment using initial public offerings on a stock market," Economics Working Paper Archive (University of Rennes 1 & University of Caen) 201331, Center for Research in Economics and Management (CREM), University of Rennes 1, University of Caen and CNRS.

    More about this item

    Keywords

    Ambiguity; Generalized Bayesian update; Learning; Dynamic consistency; Choquet expected utility; C72; D81;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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