# Partial probabilistic information

*Alain Chateauneuf* () and
*Caroline Ventura*

*Journal of Mathematical Economics*, 2011, vol. 47, issue 1, 22-28

**Abstract:**
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.

**Keywords:** Partial; probabilistic; information; Exact; capacity; Core; Extensions; of; set; functions (search for similar items in EconPapers)

**Date:** 2011

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Working Paper: Partial probabilistic information (2011)

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**Persistent link:** https://EconPapers.repec.org/RePEc:eee:mateco:v:47:y:2011:i:1:p:22-28

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