Values and Derivatives
The diagonal formula in the theory of nonatomic games expresses the idea that the Shapley value of each infinitesimal player is his marginal contribution to the worth of a “perfect sample” of the population of all players, when averaged over all possible sample sizes. The concept of marginal contribution is most easily expressed in terms of derivatives; as a result, the diagonal formula has heretofore only been established for spaces of games that are in an appropriate sense differentiable (such as p NA or p NAD). In this paper we use an averaging process to reinterpret and then prove the diagonal formula for much larger spaces of games, including spaces (like bv 'NA) in which the games cannot be considered differentiable and may even have jumps (e.g., voting games). The new diagonal formula is then used to establish the existence of values on even larger spaces of games, on which it had not previously been known that there exists any operator satisfying the axioms for the Shapley value.
Volume (Year): 5 (1980)
Issue (Month): 4 (November)
|Contact details of provider:|| Postal: 7240 Parkway Drive, Suite 300, Hanover, MD 21076 USA|
Web page: http://www.informs.org/
More information through EDIRC
When requesting a correction, please mention this item's handle: RePEc:inm:ormoor:v:5:y:1980:i:4:p:523-552. 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: (Mirko Janc)
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.