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Monotone Continuous Multiple Priors

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Author Info
Massimo Marinacci ()
Fabio Maccheroni ()
Alain Chateauneuf ()
Jean-Marc Tallon ()

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Abstract

We show that the monotone continuity condition introduced by Villegas (1964) and Arrow (1970) is the behavioral counterpart of countable additivity (and relative weak compactness) in a multiple priors model. This generalizes their original result, in which the special case of a singleton set of priors is considered. Further extending their results, we provide a behavioral counterpart for the convex rangedness of the priors (both considered singularly and as a vector measure).

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Paper provided by ICER - International Centre for Economic Research in its series ICER Working Papers - Applied Mathematics Series with number 30-2003.

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Length: 24 pages
Date of creation: Jun 2003
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Handle: RePEc:icr:wpmath:30-2003

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  1. Massimo Marinacci & Luigi Montrucchio, 2005. "Stable cores of large games," International Journal of Game Theory, Springer, vol. 33(2), pages 189-213, 06. [Downloadable!] (restricted)
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  1. Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini, 2004. "Variational representation of preferences under ambiguity," ICER Working Papers - Applied Mathematics Series 05-2004, ICER - International Centre for Economic Research. [Downloadable!]
  2. Antonio Lijoi & Igor Prünster & Stephen G. Walker, 2004. "On rates of convergence for posterior distributions in infinite–dimensional models," ICER Working Papers - Applied Mathematics Series 24-2004, ICER - International Centre for Economic Research. [Downloadable!]
  3. Massimiliano Amarante, 2003. "Ambiguity, Measurability and Multiple Priors," Discussion Papers 0203-23, Columbia University, Department of Economics. [Downloadable!]
  4. Antonio Lijoi & Igor Prünster & Stephen G. Walker, 2004. "Contributions to the understanding of Bayesian consistency," ICER Working Papers - Applied Mathematics Series 13-2004, ICER - International Centre for Economic Research. [Downloadable!]
  5. Massimiliano Amarante, 2003. "Ambiguous Events," Discussion Papers 0304-04, Columbia University, Department of Economics. [Downloadable!]
  6. Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini, 2004. "Ambiguity Aversion, Robustness, and the Variational Representation of Preferences," Carlo Alberto Notebooks 12, Collegio Carlo Alberto, revised 2006. [Downloadable!]
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  7. Massimiliano Amarante & F. Maccheroni & M. Marinacci & L. Montrucchio, 2005. "Cores of non-atomic market games," Discussion Papers 0506-10, Columbia University, Department of Economics. [Downloadable!]
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  8. Antonio Lijoi & Igor Prünster & Stephen G. Walker, 2004. "On consistency of nonparametric normal mixtures for Bayesian density estimation," ICER Working Papers - Applied Mathematics Series 23-2004, ICER - International Centre for Economic Research. [Downloadable!]
  9. Massimiliano Amarante & Emel Filiz, 2004. "Ambiguous events and Maxmin Expected Utility," Discussion Papers 0405-09, Columbia University, Department of Economics. [Downloadable!]
    Other versions:
  10. Alain Chateauneuf & Jean-Philippe Lefort, 2006. "Some Fubini theorems on sigma-algebras for non additive measures," Cahiers de la Maison des Sciences Economiques b06086, Université Panthéon-Sorbonne (Paris 1). [Downloadable!]
  11. Massimo Marinacci, 2001. "Probabilistic sophistication and multiple priors," ICER Working Papers - Applied Mathematics Series 08-2001, ICER - International Centre for Economic Research. [Downloadable!]
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  12. Massimiliano Amarante & Fabio Maccheroni, 2004. "The Knob of the Discord," Discussion Papers 0405-14, Columbia University, Department of Economics. [Downloadable!]
  13. Massimo Marinacci & Fabio Maccheroni, 2002. "How to cut a pizza fairly: fair division with descreasing marginal evaluations," ICER Working Papers - Applied Mathematics Series 23-2002, ICER - International Centre for Economic Research. [Downloadable!]
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