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Partial probabilistic information

Author

Listed:
  • Alain Chateauneuf

    (PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Caroline Ventura

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

Abstract

Suppose a decision maker (DM) has partial information about certain events of a [sigma]-algebra belonging to a set and assesses their likelihood through a capacity v. When is this information probabilistic, i.e. compatible with a probability? We consider three notions of compatibility with a probability in increasing degree of preciseness. The weakest requires the existence of a probability P on such that P(E)>=v(E) for all , we then say that v is a probability lower bound. A stronger one is to ask that v be a lower probability, that is the infimum of a family of probabilities on . The strongest notion of compatibility is for v to be an extendable probability, i.e. there exists a probability P on which coincides with v on . We give necessary and sufficient conditions on v in each case and, when is finite, we provide effective algorithms that check them in a finite number of steps.
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Suggested Citation

  • Alain Chateauneuf & Caroline Ventura, 2011. "Partial probabilistic information," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00685404, HAL.
    • Handle: RePEc:hal:cesptp:hal-00685404
    DOI: 10.1016/j.jmateco.2010.09.007
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    References listed on IDEAS

    as
    1. Nehring, Klaus, 1999. "Capacities and probabilistic beliefs: a precarious coexistence," Mathematical Social Sciences, Elsevier, vol. 38(2), pages 197-213, September.
    2. DELBAEN, Freddy, 1974. "Convex games and extreme points," LIDAM Reprints CORE 159, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Yaron Azrieli & Ehud Lehrer, 2007. "Extendable Cooperative Games," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 9(6), pages 1069-1078, December.
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