Document Type
Report
Source Publication Title
Technical Report 338
Abstract
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.
Disciplines
Mathematics | Physical Sciences and Mathematics
Publication Date
9-1-1999
Language
English
License
This work is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 4.0 International License.
Recommended Citation
Martínez-Legaz, Juan-Enrique and Dragan, Irinel C., "On the Semivalues and the Power Core of Cooperative TU Games" (1999). Mathematics Technical Papers. 15.
https://mavmatrix.uta.edu/math_technicalpapers/15