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Partial probabilistic information

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  • Chateauneuf, Alain
  • Ventura, Caroline

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.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 47 (2011)
Issue (Month): 1 (January)
Pages: 22-28

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Handle: RePEc:eee:mateco:v:47:y:2011:i:1:p:22-28

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Web page: http://www.elsevier.com/locate/jmateco

Related research

Keywords: Partial probabilistic information Exact capacity Core Extensions of set functions;

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  1. Nehring, Klaus, 1999. "Capacities and probabilistic beliefs: a precarious coexistence," Mathematical Social Sciences, Elsevier, Elsevier, vol. 38(2), pages 197-213, September.
  2. Yaron Azrieli & Ehud Lehrer, 2007. "Extendable Cooperative Games," Journal of Public Economic Theory, Association for Public Economic Theory, Association for Public Economic Theory, vol. 9(6), pages 1069-1078, December.
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