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- A Bayesian Approach To Uncertainty Aversion

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Author Info
Vincent Feltkamp (Statistics Netherlands)
Yoram Halevy (University of Pennsylvania)

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Abstract

The Ellsberg paradox demonstrates that peoples belief over uncertainevents might not be representable by subjective probability. We relate this paradox to other commonly observed anomalies, suchas a rejection of the backward induction prediction in the one-shot Ultimatum Game. We argue that the pattern common to theseobservations is that the behavior is governed by rational rules. These rules have evolved and are optimal within the repeated andconcurrent environments that people usually encounter. When an individual relies on these rules to analyzeone-shot or single circumstances, paradoxes emerge. We show that when a risk averse individualhas a Bayesian prior and uses a rule which is optimal for simultaneous and positively correlatedambiguous risks to evaluate a single vague circumstance, his behavior will exhibit uncertaintyaversion. Thus, the behavior predicted by Ellsberg may be explained within the Bayesian expectedutility paradigm.

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Publisher Info
Paper provided by Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie) in its series Working Papers. Serie AD with number 1999-14.

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Length: 23 pages
Date of creation: Sep 1999
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Publication status: Published by Ivie
Handle: RePEc:ivi:wpasad:1999-14

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Keywords: Ellsberg paradox; rule rationality; ambiguity aversion; risk aversion;

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Aumann, Robert J., 1997. "Rationality and Bounded Rationality," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 2-14, October. [Downloadable!] (restricted)
  2. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April. [Downloadable!] (restricted)
  3. Machina, Mark J & Schmeidler, David, 1992. "A More Robust Definition of Subjective Probability," Econometrica, Econometric Society, vol. 60(4), pages 745-80, July. [Downloadable!] (restricted)
    Other versions:
  4. Ghirardato, Paolo & Klibanoff, Peter & Marinacci, Massimo, 1998. "Additivity with multiple priors," Journal of Mathematical Economics, Elsevier, vol. 30(4), pages 405-420, November. [Downloadable!] (restricted)
  5. Larry Epstein, 1997. "Uncertainty Aversion," Working Papers epstein-97-01, University of Toronto, Department of Economics. [Downloadable!]
  6. Haluk Ergin & Faruk Gul, 2003. "A Subjective Theory of Compound Lotteries," Levine's Bibliography 506439000000000406, UCLA Department of Economics. [Downloadable!]
    Other versions:
  7. Ross, Stephen A., 1999. "Adding Risks: Samuelson's Fallacy of Large Numbers Revisited," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(03), pages 323-339, September. [Downloadable!]
  8. Gilboa, Itzhak, 1987. "Expected utility with purely subjective non-additive probabilities," Journal of Mathematical Economics, Elsevier, vol. 16(1), pages 65-88, February. [Downloadable!] (restricted)
  9. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-87, May. [Downloadable!] (restricted)
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  14. Epstein, Larry G & Zhang, Jiankang, 2001. "Subjective Probabilities on Subjectively Unambiguous Events," Econometrica, Econometric Society, vol. 69(2), pages 265-306, March.
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  15. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January. [Downloadable!] (restricted)
  16. Sarin, Rakesh & Wakker, Peter, 1997. "A Single-Stage Approach to Anscombe and Aumann's Expected Utility," Review of Economic Studies, Blackwell Publishing, vol. 64(3), pages 399-409, July. [Downloadable!] (restricted)
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  17. Peter Klibanoff & Massimo Marinacci & Sujoy Mukerji, 2002. "A smooth model of decision making under ambiguity," ICER Working Papers - Applied Mathematics Series 11-2003, ICER - International Centre for Economic Research, revised Apr 2003. [Downloadable!]
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  18. Rubinstein, Ariel, 1988. "Similarity and decision-making under risk (is there a utility theory resolution to the Allais paradox?)," Journal of Economic Theory, Elsevier, vol. 46(1), pages 145-153, October. [Downloadable!] (restricted)
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    Other versions:
  22. Epstein, Larry G, 1999. "A Definition of Uncertainty Aversion," Review of Economic Studies, Blackwell Publishing, vol. 66(3), pages 579-608, July. [Downloadable!] (restricted)
  23. Sarin, Rakesh K & Wakker, Peter, 1992. "A Simple Axiomatization of Nonadditive Expected Utility," Econometrica, Econometric Society, vol. 60(6), pages 1255-72, November. [Downloadable!] (restricted)
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  27. Heiner, Ronald A, 1983. "The Origin of Predictable Behavior," American Economic Review, American Economic Association, vol. 73(4), pages 560-95, September. [Downloadable!] (restricted)
  28. Segal, Uzi, 1990. "Two-Stage Lotteries without the Reduction Axiom," Econometrica, Econometric Society, vol. 58(2), pages 349-77, March. [Downloadable!] (restricted)
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  29. Chew, S H & Epstein, Larry G, 1988. " The Law of Large Numbers and the Attractiveness of Compound Gambles," Journal of Risk and Uncertainty, Springer, vol. 1(1), pages 125-32, March.
Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Alfred Müller & Marco Scarsini, 2002. "Even Risk-Averters may Love Risk," Theory and Decision, Springer, vol. 52(1), pages 81-99, February. [Downloadable!] (restricted)
  2. Halevy, Yoram & Ozdenoren, Emre, 2008. "Uncertainty and Compound Lotteries: Calibration," Micro Theory Working Papers yoram_halevy-2008-7, Microeconomics.ca Website, revised 17 Jun 2008. [Downloadable!]
  3. Rick Harbaugh, 2005. "Prospect Theory or Skill Signaling?," Working Papers 2005-06, Indiana University, Kelley School of Business, Department of Business Economics and Public Policy. [Downloadable!]
  4. Zvi Safra & Uzi Segal, 2005. "Are Universal Preferences Possible? Calibration Results for Non-Expected Utility Theories," Boston College Working Papers in Economics 633, Boston College Department of Economics. [Downloadable!]
  5. Halevy, Yoram, 2005. "Ellsberg Revisited: an Experimental Study," Micro Theory Working Papers halevy-05-07-26-11-51-13, Microeconomics.ca Website, revised 07 Jun 2008. [Downloadable!]
    Other versions:
  6. Pierre Fleckinger, 2007. "On Multiagent Moral Hazard under Technological Uncertainty," Working Papers hal-00240716_v1, HAL. [Downloadable!]
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