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Multiple Priors as Similarity Weighted Frequencies

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  • Eichberger, Jurgen
  • Guerdjikova, Ani

Abstract

In this paper, we consider a decision-maker who tries to learn the distribution of outcomes from previously observed cases. For each observed sequence of cases, the decision-maker entertains a set of priors expressing his hypotheses about the underlying probability distribution. The set of probability distributions shrinks when new information confirms old data. We impose a version of the concatenation axiom introduced in BILLOT, GILBOA, SAMET AND SCHMEIDLER (2005) which insures 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.

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Bibliographic Info

Paper provided by Cornell University, Center for Analytic Economics in its series Working Papers with number 07-03.

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Date of creation: Apr 2007
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Handle: RePEc:ecl:corcae:07-03

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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. 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.
  3. Thibault Gajdos & Takashi Hayashi & Jean-Marc Tallon & Jean-Christophe Vergnaud, 2006. "Attitude toward imprecise information," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00130179, HAL.
  4. 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.
  5. Larry Epstein & Martin Schneider, 2002. "Learning Under Ambiguity," RCER Working Papers 497, University of Rochester - Center for Economic Research (RCER), revised Mar 2005.
  6. Nehring,K. und C.Puppe, 1999. "A Theory of Diversity," Discussion Paper Serie A 605, University of Bonn, Germany.
  7. 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.
  8. Itzhak Gilboa & Offer Lieberman & David Schmeidler, 2004. "Empirical Similarity," Cowles Foundation Discussion Papers 1486, Cowles Foundation for Research in Economics, Yale University.
  9. Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo, 2004. "Differentiating ambiguity and ambiguity attitude," Journal of Economic Theory, Elsevier, vol. 118(2), pages 133-173, October.
  10. Guerdjikova, Ani, 2008. "Case-based learning with different similarity functions," Games and Economic Behavior, Elsevier, vol. 63(1), pages 107-132, May.
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