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Case-based belief formation under ambiguity

  • Eichberger, Jürgen
  • Guerdjikova, Ani

In this paper, we consider a decision maker who tries to learn the distribution of outcomes from previously observed cases. For each observed database of cases the decision maker predicts a set of priors expressing his beliefs about the underlying probability distribution. We impose a version of the concatenation axiom introduced in Billot et al. (2005) which ensures that the sets of priors can be represented as a weighted sum of the observed frequencies of cases. The weights are the uniquely determined similarities between the observed cases and the case under investigation. The predicted probabilities, however, may vary with the number of observations. This generalization of Billot et al. (2005) allows one to model learning processes.

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Article provided by Elsevier in its journal Mathematical Social Sciences.

Volume (Year): 60 (2010)
Issue (Month): 3 (November)
Pages: 161-177

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Handle: RePEc:eee:matsoc:v:60:y:2010:i:3:p:161-177
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/505565

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  1. 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.
  2. Itzhak Gilboa & David Schmeidler & Offer Lieberman, 2006. "Empirical Similarity," Post-Print hal-00746558, HAL.
  3. Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo, 2004. "Differentiating ambiguity and ambiguity attitude," Journal of Economic Theory, Elsevier, vol. 118(2), pages 133-173, October.
  4. Antoine Billot & Itzhak Gilboa & Dov Samet & David Schmeidler, 2004. "Probabilities as Similarity-Weighted Frequencies," Levine's Bibliography 122247000000000696, UCLA Department of Economics.
  5. 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.
  6. Gilboa,Itzhak & Schmeidler,David, 2001. "A Theory of Case-Based Decisions," Cambridge Books, Cambridge University Press, number 9780521802345, November.
  7. David S. Ahn, 2008. "Ambiguity Without a State Space," Review of Economic Studies, Oxford University Press, vol. 75(1), pages 3-28.
  8. Thibault Gajdos & Takashi Hayashi & Jean-Marc Tallon & Jean-Christophe Vergnaud, 2008. "Attitude toward imprecise information," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00451982, HAL.
  9. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-87, May.
  10. David Schmeidler, 2000. "Utility in Case-Based Decision Theory," Working Papers 00-06, Ohio State University, Department of Economics.
  11. Larry Epstein & Martin Schneider, 2006. "Learning Under Ambiguity," RCER Working Papers 527, University of Rochester - Center for Economic Research (RCER).
  12. Truman F. Bewley, 1986. "Knightian Decision Theory: Part 1," Cowles Foundation Discussion Papers 807, Cowles Foundation for Research in Economics, Yale University.
  13. Eichberger, Jürgen & Guerdjikova, Ani, 2008. "Case-based expected utility : preferences over actions and data," Papers 08-32, Sonderforschungsbreich 504.
  14. 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.
  15. Eichberger, Jürgen & Guerdjikova, Ani, 2008. "Case-Based Expected Utility: Preferences over Actions and Data," Sonderforschungsbereich 504 Publications 08-32, Sonderforschungsbereich 504, Universität Mannheim;Sonderforschungsbereich 504, University of Mannheim.
  16. Gilboa,Itzhak, 2009. "Theory of Decision under Uncertainty," Cambridge Books, Cambridge University Press, number 9780521517324, November.
  17. Daniel Ellsberg, 2000. "Risk, Ambiguity and the Savage Axioms," Levine's Working Paper Archive 7605, David K. Levine.
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