Variations on the shapley value
In: Handbook of Game Theory with Economic Applications
This survey captures the main contributions in the area described by the title that were published up to 1997. (Unfortunately, it does not capture all of them.) The variations that are the subject of this chapter are those axiomatically characterized solutions which are obtained by varying either the set of axioms that define the Shapley value, or the domain over which this value is defined, or both.In the first category, we deal mainly with probabilistic values. These are solutions that preserve one of the essential features of the Shapley value, namely, that they are given, for each player, by some averaging of the player's marginal contributions to coalitions, where the probabilistic weights depend on the coalitions only and not on the game. The Shapley value is the unique probabilistic value that is efficient and symmetric. We characterize and discuss two families of solutions: quasivalues, which are efficient probabilistic values, and semivalues, which are symmetric probabilistic values.In the second category, we deal with solutions that generalize the Shapley value by changing the domain over which the solution is defined. In such generalizations the solution is defined on pairs, consisting of a game and some structure on the set of players. The Shapley value is a special case of such a generalization in the sense that it coincides with the solution on the restricted domain in which the second argument is fixed to be the "trivial" one. Under this category we survey mostly solutions in which the structure is a partition of the set of the players, and a solution in which the structure is a graph, the vertices of which are the players.
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.
|This chapter was published in: ||This item is provided by Elsevier in its series Handbook of Game Theory with Economic Applications with number
3-54.||Handle:|| RePEc:eee:gamchp:3-54||Contact details of provider:|| Web page: http://www.elsevier.com/wps/find/bookseriesdescription.cws_home/BS_HE/description |
When requesting a correction, please mention this item's handle: RePEc:eee:gamchp:3-54. 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: (Zhang, Lei)
If references are entirely missing, you can add them using this form.