Generalized Shapely Value for Games with a Coalition Structure

Somdeb Lahiri

IIMA Working Papers from Indian Institute of Management Ahmedabad, Research and Publication Department

Abstract: In cooperative games with transferable utility, there is usually no restriction on the possible coalitions that can materialize. A significant departure from this tradition, occurs in Moulin [1995], where the concept of admissible coalitions arise. In this paper we consider cooperative games with admissible coalitions, requiring that both the grand coalition, as well as, the null coalition are always admissible. We call such games, ‘games with a coalition structure’. We define the concept of a core for such games and introduce a generalization of the notion of Shapley value. We define this generalized Shapley value to be the unique value satisfying the Dummy Player Property, Anonymity and Linearity. All these properties have been adapted from the standard context to our framework in such a way, that the existence of a unique value satisfying these properties is guaranteed. We subsequently consider specific coalition structures and obtain closed form solutions for the generalized Shapley value in each case.

Date: 1997-09-01
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:iim:iimawp:wp01469

Access Statistics for this paper

More papers in IIMA Working Papers from Indian Institute of Management Ahmedabad, Research and Publication Department Contact information at EDIRC.
Bibliographic data for series maintained by ().