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Multiple Priors as Similarity Weighted Frequencies

  • Jürgen Eichberger

    ()

    (University of Heidelberg, Department of Economics)

  • Ani Guerdjikova

    ()

    (Cornell University, Department of Economics)

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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File URL: http://www.uni-heidelberg.de/md/awi/forschung/dp470.pdf
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Paper provided by University of Heidelberg, Department of Economics in its series Working Papers with number 0470.

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Length: 39 pages
Date of creation: Jul 2008
Date of revision: Jul 2008
Handle: RePEc:awi:wpaper:0470
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  1. Larry Epstein & Martin Schneider, 2002. "Learning Under Ambiguity," RCER Working Papers 497, University of Rochester - Center for Economic Research (RCER), revised Mar 2005.
  2. 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).
  3. Itzhak Gilboa & Offer Lieberman & David Schmeidler, 2006. "Empirical Similarity," The Review of Economics and Statistics, MIT Press, vol. 88(3), pages 433-444, August.
  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. Antoine Billot & Itzhak Gilboa & Dov Samet & David Schmeidler, 2005. "Probabilities as Similarity-Weighted Frequencies," Econometrica, Econometric Society, vol. 73(4), pages 1125-1136, 07.
  6. 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.
  7. Klaus Nehring & Clemens Puppe, 2002. "A Theory of Diversity," Econometrica, Econometric Society, vol. 70(3), pages 1155-1198, May.
  8. Peter Klibanoff & Massimo Marinacci & Sujoy Mukerji, 2005. "A Smooth Model of Decision Making under Ambiguity," Econometrica, Econometric Society, vol. 73(6), pages 1849-1892, November.
  9. Guerdjikova, Ani, 2008. "Case-based learning with different similarity functions," Games and Economic Behavior, Elsevier, vol. 63(1), pages 107-132, May.
  10. Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo, 2004. "Differentiating ambiguity and ambiguity attitude," Journal of Economic Theory, Elsevier, vol. 118(2), pages 133-173, October.
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