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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. 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. 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.
  3. Itzhak Gilboa & David Schmeidler & Offer Lieberman, 2006. "Empirical Similarity," Post-Print hal-00746558, HAL.
  4. Antoine Billot & Itzhak Gilboa & David Schmeidler & Dov Samet, 2004. "Probabilities as Similarity-Weighted Frequencies," Cowles Foundation Discussion Papers 1492, Cowles Foundation for Research in Economics, Yale University.
  5. 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.
  6. 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.
  7. Gilboa,Itzhak, 2009. "Theory of Decision under Uncertainty," Cambridge Books, Cambridge University Press, number 9780521741231, October.
  8. Larry Epstein & Martin Schneider, 2002. "Learning Under Ambiguity," RCER Working Papers 497, University of Rochester - Center for Economic Research (RCER), revised Mar 2005.
  9. Truman F. Bewley, 1986. "Knightian Decision Theory: Part 1," Cowles Foundation Discussion Papers 807, Cowles Foundation for Research in Economics, Yale University.
  10. Gilboa,Itzhak & Schmeidler,David, 2001. "A Theory of Case-Based Decisions," Cambridge Books, Cambridge University Press, number 9780521003117, October.
  11. David Schmeidler, 1989. "Subjective Probability and Expected Utility without Additivity," Levine's Working Paper Archive 7662, David K. Levine.
  12. Daniel Ellsberg, 2000. "Risk, Ambiguity and the Savage Axioms," Levine's Working Paper Archive 7605, David K. Levine.
  13. David S. Ahn, 2008. "Ambiguity Without a State Space," Review of Economic Studies, Oxford University Press, vol. 75(1), pages 3-28.
  14. Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo, 2004. "Differentiating ambiguity and ambiguity attitude," Journal of Economic Theory, Elsevier, vol. 118(2), pages 133-173, October.
  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 & Schmeidler, David & Wakker, Peter P., 2002. "Utility in Case-Based Decision Theory," Journal of Economic Theory, Elsevier, vol. 105(2), pages 483-502, August.
  17. Eichberger, Jürgen & Guerdjikova, Ani, 2008. "Case-based expected utility : preferences over actions and data," Papers 08-32, Sonderforschungsbreich 504.
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