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The ambiguity triangle: uncovering fundamental patterns of behavior under uncertainty

Author

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  • Daniel R. Burghart
  • Thomas Epper
  • Ernst Fehr

Abstract

The probability triangle (also called the Marschak-Machina triangle) allows for compact and intuitive depictions of risk preferences. Here, we develop an analogous tool for choice under uncertainty - the ambiguity triangle - and show that indifference curves in this triangle capture preferences for unknown probabilities. In particular, the ambiguity triangle allows us to examine whether subjects adhere to the generalized axiom of revealed preference (GARP) and satisfy a non-parametric test for constant ambiguity attitudes. We find that more than 95% of subjects adhere to GARP and that about 60% satisfy our test for a constant ambiguity attitude. Yet, among these 60% of subjects there is substantial preference heterogeneity. We characterize this heterogeneity with finite-mixture estimates of a one-parameter extension of Expected Utility Theory wherein 48% of subjects are ambiguity averse, 22% are ambiguity seeking, and 30% are close to ambiguity neutral. The ambiguity triangle also highlights how variable ambiguity attitudes arise mainly because indifference curves are ’fanning-in’ across the triangle. This fanning-in property implies that aversion to ambiguity increases as the likelihood of receiving a good outcome increases. We capture this behavior with a simple parametric model that also allows for finite mixture characterizations of preference heterogeneity for these subjects. We show that for a substantial share of these subjects (43%) their fanning-in is so strong that, although they are initially ambiguity seeking, they become strongly ambiguity averse as the likelihood of receiving a good outcome increases.

Suggested Citation

  • Daniel R. Burghart & Thomas Epper & Ernst Fehr, 2015. "The ambiguity triangle: uncovering fundamental patterns of behavior under uncertainty," ECON - Working Papers 196, Department of Economics - University of Zurich.
  • Handle: RePEc:zur:econwp:196
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    File URL: http://www.econ.uzh.ch/static/wp/econwp196.pdf
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    References listed on IDEAS

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    1. repec:wsi:wschap:9789813235816_0006 is not listed on IDEAS
    2. Daniel Houser & Michael Keane & Kevin McCabe, 2004. "Behavior in a Dynamic Decision Problem: An Analysis of Experimental Evidence Using a Bayesian Type Classification Algorithm," Econometrica, Econometric Society, vol. 72(3), pages 781-822, May.
    3. Mohammed Abdellaoui & Aurelien Baillon & Laetitia Placido & Peter P. Wakker, 2011. "The Rich Domain of Uncertainty: Source Functions and Their Experimental Implementation," American Economic Review, American Economic Association, vol. 101(2), pages 695-723, April.
    4. Daniel R. Burghart & Thomas Epper & Ernst Fehr, 2014. "The two faces of independence: betweenness and homotheticity," ECON - Working Papers 179, Department of Economics - University of Zurich.
    5. David S. Ahn, 2008. "Ambiguity Without a State Space," Review of Economic Studies, Oxford University Press, vol. 75(1), pages 3-28.
    6. John Hey & Noemi Pace, 2014. "The explanatory and predictive power of non two-stage-probability theories of decision making under ambiguity," Journal of Risk and Uncertainty, Springer, vol. 49(1), pages 1-29, August.
    7. Conte, Anna & Hey, John D. & Moffatt, Peter G., 2011. "Mixture models of choice under risk," Journal of Econometrics, Elsevier, vol. 162(1), pages 79-88, May.
    8. repec:wsi:wschap:9789813235816_0008 is not listed on IDEAS
    9. Helga Fehr-Duda & Thomas Epper, 2012. "Probability and Risk: Foundations and Economic Implications of Probability-Dependent Risk Preferences," Annual Review of Economics, Annual Reviews, vol. 4(1), pages 567-593, July.
    10. Johanna Etner & Meglena Jeleva & Jean‐Marc Tallon, 2012. "Decision Theory Under Ambiguity," Journal of Economic Surveys, Wiley Blackwell, vol. 26(2), pages 234-270, April.
    11. Helga Fehr-Duda & Adrian Bruhin & Thomas Epper & Renate Schubert, 2010. "Rationality on the rise: Why relative risk aversion increases with stake size," Journal of Risk and Uncertainty, Springer, vol. 40(2), pages 147-180, April.
    12. John Hey & Gianna Lotito & Anna Maffioletti, 2010. "The descriptive and predictive adequacy of theories of decision making under uncertainty/ambiguity," Journal of Risk and Uncertainty, Springer, vol. 41(2), pages 81-111, October.
    13. repec:wsi:wschap:9789813235816_0001 is not listed on IDEAS
    14. Dumav, Martin & Stinchcombe, Maxwell B., 2014. "The von Neumann/Morgenstern approach to ambiguity," Center for Mathematical Economics Working Papers 480, Center for Mathematical Economics, Bielefeld University.
    15. Dobbs, Ian M, 1991. "A Bayesian Approach to Decision-Making under Ambiguity," Economica, London School of Economics and Political Science, vol. 58(232), pages 417-440, November.
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    Cited by:

    1. Konstantinos Georgalos, 2016. "Dynamic decision making under ambiguity," Working Papers 112111041, Lancaster University Management School, Economics Department.
    2. repec:eee:ecolet:v:167:y:2018:i:c:p:43-47 is not listed on IDEAS

    More about this item

    Keywords

    Behavior under uncertainty; ambiguity preferences; heterogeneity; probability triangle; ambiguity triangle;

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • C91 - Mathematical and Quantitative Methods - - Design of Experiments - - - Laboratory, Individual Behavior

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