Partial probabilistic information
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.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Klaus Nehring & Michael Magill & Julian R. Betts, 2003.
"Capacities And Probabilistic Beliefs: A Precarious Coexistence,"
978, University of California, Davis, Department of Economics.
- Nehring, Klaus, 1999. "Capacities and probabilistic beliefs: a precarious coexistence," Mathematical Social Sciences, Elsevier, vol. 38(2), pages 197-213, September.
- Klaus Nehring, "undated". "Capacities And Probabilistic Beliefs: A Precarious Coexistence," Department of Economics 97-08, California Davis - Department of Economics.
- 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.
When requesting a correction, please mention this item's handle: RePEc:eee:mateco:v:47:y:2011:i:1:p:22-28. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.