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Multiple Priors as Similarity Weighted Frequencies

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Author Info
Eichberger, Jürgen () (Sonderforschungsbereich 504)
Guerdjikova, Ani () (Cornell University)
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 predicts a set of priors expressing his beliefs about the underlying probability distribution. 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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Paper provided by Sonderforschungsbereich 504, Universität Mannheim & Sonderforschungsbereich 504, University of Mannheim in its series Sonderforschungsbereich 504 Publications with number 08-07.

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Length: 39 pages
Date of creation: 26 May 2008
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Handle: RePEc:xrs:sfbmaa:08-07

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  1. Larry Epstein & Martin Schneider, 2006. "Learning Under Ambiguity," RCER Working Papers 527, University of Rochester - Center for Economic Research (RCER). [Downloadable!]
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  2. 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. [Downloadable!] (restricted)
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  3. Guerdjikova, Ani, 2008. "Case-based learning with different similarity functions," Games and Economic Behavior, Elsevier, vol. 63(1), pages 107-132, May. [Downloadable!] (restricted)
  4. Antoine Billot & Itzhak Gilboa & Dov Samet & David Schmeidler, 2005. "Probabilities as Similarity-Weighted Frequencies," Econometrica, Econometric Society, vol. 73(4), pages 1125-1136, 07. [Downloadable!] (restricted)
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  5. Klaus Nehring & Clemens Puppe, 2002. "A Theory of Diversity," Econometrica, Econometric Society, vol. 70(3), pages 1155-1198, May. [Downloadable!] (restricted)
  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. [Downloadable!]
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  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). [Downloadable!]
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  8. 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. [Downloadable!] (restricted)
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  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. [Downloadable!] (restricted)
  10. Itzhak Gilboa & Offer Lieberman & David Schmeidler, 2004. "Empirical Similarity," Cowles Foundation Discussion Papers 1486, Cowles Foundation, Yale University. [Downloadable!]
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