Reference : Weighted Banzhaf power and interaction indexes through weighted approximations of games
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
Business & economic sciences : Quantitative methods in economics & management
http://hdl.handle.net/10993/1462
Weighted Banzhaf power and interaction indexes through weighted approximations of games
English
Marichal, Jean-Luc mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Mathonet, Pierre mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
1-Jun-2011
European Journal of Operational Research
Elsevier Science
211
2
352-358
Yes (verified by ORBilu)
International
0377-2217
Amsterdam
The Netherlands
[en] Cooperative game ; Pseudo-Boolean function ; Power index ; Interaction index ; Least squares approximation
[en] The Banzhaf power index was introduced in cooperative game theory to measure the real power of players in a game. The Banzhaf interaction index was then proposed to measure the interaction degree inside coalitions of players. It was shown that the power and interaction indexes can be obtained as solutions of a standard least squares approximation problem for pseudo-Boolean functions. Considering certain weighted versions of this approximation problem, we define a class of weighted interaction indexes that generalize the Banzhaf interaction index. We show that these indexes define a subclass of the family of probabilistic interaction indexes and study their most important properties. Finally, we give an interpretation of the Banzhaf and Shapley interaction indexes as centers of mass of this subclass of interaction indexes.
Mathematics Research Unit (FSTC)
University of Luxembourg - UL
Researchers ; Professionals ; Students
http://hdl.handle.net/10993/1462
10.1016/j.ejor.2010.11.027
http://arxiv.org/abs/1001.3052

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