IDEAS home Printed from
MyIDEAS: Log in (now much improved!) to save this article

Weber Polyhedron And Weighted Shapley Values

Listed author(s):


    (Sobolev Institute of Mathematics, Prosp. Koptyuga 4, 630090 Novosibirsk, Russia)

In this paper, we consider the relationship between the Weber set and the Shapley set being the set of all weighted Shapley values of a TU-game. In particular, we propose a new proof for the fact that the Weber set always includes the Shapley set. It is shown that the inclusion mentioned follows directly from the representation theorem for the Weber set, established by Vasil'ev and van der Laan (2002), Siberian Adv. Math., V.12, N2, 97–125. Since the representation theorem applied is formulated in terms of the dividend sharing systems belonging to the so-called Weber polyhedron, we pay strong attention to some monotonicity properties of this polyhedron. Specifically, by making use of induction techniques, a new proof of the strong monotonicity of the Weber d-systems is obtained, and a simplified description of the Weber polyhedron is given.

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.

File URL:
Download Restriction: Access to full text is restricted to subscribers.

File URL:
Download Restriction: Access to full text is restricted to subscribers.

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.

Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal International Game Theory Review.

Volume (Year): 09 (2007)
Issue (Month): 01 ()
Pages: 139-150

in new window

Handle: RePEc:wsi:igtrxx:v:09:y:2007:i:01:p:139-150
Contact details of provider: Web page:

Order Information: Email:

No references listed on IDEAS
You can help add them by filling out this form.

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:wsi:igtrxx:v:09:y:2007:i:01:p:139-150. 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: (Tai Tone Lim)

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.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.