Document Type


Source Publication Title

Technical Report 338


The Semivalues were introduced axiomatically by P.Dubey, A.Neyman and R.J.Weber (1981) as an important class of values for cooperative TU games. This class contains the Shapley value, the Banzhaf value, and many other values. For the Shapley value characterizations of games for which the Shapley value is coalitionally rational are due to Inarra and Usategui (1993), Izawa and Takahashi (1998), and Marin-Solano and Rafels (1999). In this paper the same problem of coalitional rationality is discussed for Semivalues, by using special formulas for the computation of Semivalues. The characterization shows that this is a prosperity property as defined by Van Gellekom, Potters and Reijnierse (1999) and a threshold for the property can be computed by using averages per capita. A characterization in terms of the Potential game is also given, by using concepts of average convexity and weak average convexity.


Mathematics | Physical Sciences and Mathematics

Publication Date




Included in

Mathematics Commons



To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.