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About partial probabilistic information

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Abstract

Suppose a decision maker (DM) has partial information about certain events of a ?-algebra A belonging to 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 A such that P(E)? v(E) for all E ? ?, we then say that v is a probability minorant. A stronger one is to ask that v be a lower probability, that is the infimum of a family of probabilities on A. The strongest notion of compatibility is for v to be an extendable probability, i.e. there exists a probability P on A which coincides with v on A. 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

Suggested Citation

  • Alain Chateauneuf & Caroline Ventura, 2009. "About partial probabilistic information," Documents de travail du Centre d'Economie de la Sorbonne 09082, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    • Handle: RePEc:mse:cesdoc:09082
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    Keywords

    Partial probabilistic information; exact capacity; core; extensions of set functions;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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