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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. Gilboa,Itzhak & Schmeidler,David, 2001. "A Theory of Case-Based Decisions," Cambridge Books, Cambridge University Press, number 9780521003117.
  2. Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo, 2004. "Differentiating ambiguity and ambiguity attitude," Journal of Economic Theory, Elsevier, vol. 118(2), pages 133-173, October.
  3. Larry G. Epstein & Martin Schneider, 2007. "Learning Under Ambiguity," Review of Economic Studies, Oxford University Press, vol. 74(4), pages 1275-1303.
  4. Gilboa,Itzhak, 2009. "Theory of Decision under Uncertainty," Cambridge Books, Cambridge University Press, number 9780521741231.
  5. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-87, May.
  6. 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.
  7. Thibault Gajdos & Takashi Hayashi & Jean-Marc Tallon & Jean-Christophe Vergnaud, 2006. "Attitude toward imprecise information," Cahiers de la Maison des Sciences Economiques v06081, Université Panthéon-Sorbonne (Paris 1).
  8. 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.
  9. Sujoy Mukerji & Peter Klibanoff, 2002. "A Smooth Model of Decision,Making Under Ambiguity," Economics Series Working Papers 113, University of Oxford, Department of Economics.
  10. Itzhak Gilboa & Offer Lieberman & David Schmeidler, 2004. "Empirical Similarity," Cowles Foundation Discussion Papers 1486, Cowles Foundation for Research in Economics, Yale University.
  11. 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.
  12. Antoine Billot & Itzhak Gilboa & Dov Samet & David Schmeidler, 2004. "Probabilities as Similarity-Weighted Frequencies," Levine's Bibliography 122247000000000696, UCLA Department of Economics.
  13. Daniel Ellsberg, 2000. "Risk, Ambiguity and the Savage Axioms," Levine's Working Paper Archive 7605, David K. Levine.
  14. David S. Ahn, 2008. "Ambiguity Without a State Space," Review of Economic Studies, Oxford University Press, vol. 75(1), pages 3-28.
  15. Truman F. Bewley, 1986. "Knightian Decision Theory: Part 1," Cowles Foundation Discussion Papers 807, Cowles Foundation for Research in Economics, Yale University.
  16. David Schmeidler, 2000. "Utility in Case-Based Decision Theory," Working Papers 00-06, Ohio State University, Department of Economics.
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