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Ambiguity, Data and Preferences for Information - A Case-Based Approach

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  • Ani Guerdjikova
  • Jürgen Eichberger

    () (THEMA, Universite de Cergy-Pontoise and THEMA, University of Heidelberg)

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    Abstract

    In this paper we suggest a behavioral approach to decision making under ambiguity based on available information. A decision situation is characterized by a set of actions, a set of outcomes, and data consisting of action-outcome pairs. Decision-makers express preferences over actions and data sets. We derive a representation of preferences, which separates utility and beliefs. While the utility function is purely subjective, the beliefs of the decision maker combine objective characteristics of the data (number and frequency of observations) with subjective features of the decision maker (similarity of observations and perceived ambiguity). We identify the subjectively perceived degree of ambiguity and separate it into ambiguity due to a limited number of observations and ambiguity due to data heterogeneity. We also determine the decision maker’s attitude towards ambiguity. The special case of no ambiguity represents beliefs as similarity-weighted frequencies and provides a behavioral foundation for Billot, Gilboa, Samet and Schmeidler’s (2005) representation.

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    Bibliographic Info

    Paper provided by THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise in its series THEMA Working Papers with number 2012-45 Classification-Jel.

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    Date of creation: 2012
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    Handle: RePEc:ema:worpap:2012-45

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    1. Chateauneuf, Alain & Eichberger, Jürgen & Grant, Simon, 2003. "Choice under Uncertainty with the Best and Worst in Mind: Neo-additive Capacities," Sonderforschungsbereich 504 Publications 03-10, Sonderforschungsbereich 504, Universität Mannheim & Sonderforschungsbereich 504, University of Mannheim.
    2. David S. Ahn, 2008. "Ambiguity Without a State Space," Review of Economic Studies, Wiley Blackwell, vol. 75(1), pages 3-28, 01.
    3. David Schmeidler, 2000. "Utility in Case-Based Decision Theory," Working Papers 00-06, Ohio State University, Department of Economics.
    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. Gilboa,Itzhak & Schmeidler,David, 2001. "A Theory of Case-Based Decisions," Cambridge Books, Cambridge University Press, number 9780521003117.
    6. Larry G. Epstein & Martin Schneider, 2007. "Learning Under Ambiguity," Review of Economic Studies, Wiley Blackwell, vol. 74(4), pages 1275-1303, October.
    7. Itzhak Gilboa & Offer Lieberman & David Schmeidler, 2006. "Empirical Similarity," The Review of Economics and Statistics, MIT Press, vol. 88(3), pages 433-444, August.
    8. Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo, 2004. "Differentiating ambiguity and ambiguity attitude," Journal of Economic Theory, Elsevier, vol. 118(2), pages 133-173, October.
    9. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    10. Antoine Billot & Itzhak Gilboa & Dov Samet & David Schmeidler, 2005. "Probabilities as Similarity-Weighted Frequencies," Econometrica, Econometric Society, vol. 73(4), pages 1125-1136, 07.
    11. David Schmeidler, 1989. "Subjective Probability and Expected Utility without Additivity," Levine's Working Paper Archive 7662, David K. Levine.
    12. Manski, Charles F., 2000. "Identification problems and decisions under ambiguity: Empirical analysis of treatment response and normative analysis of treatment choice," Journal of Econometrics, Elsevier, vol. 95(2), pages 415-442, April.
    13. Daniel Ellsberg, 2000. "Risk, Ambiguity and the Savage Axioms," Levine's Working Paper Archive 7605, David K. Levine.
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