Reference : Influence and interaction indexes in cooperative games: a unified least squares approach
Scientific congresses, symposiums and conference proceedings : Unpublished conference
Physical, chemical, mathematical & earth Sciences : Mathematics Business & economic sciences : Quantitative methods in economics & management
http://hdl.handle.net/10993/7226
Influence and interaction indexes in cooperative games: a unified least squares approach
English
Marichal, Jean-Luc[University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Mathonet, Pierre[University of Liège, Belgium > Department of Mathematics]
10-Nov-2011
No
Yes
International
5th seminar “Ordered Structures in Games And Decision” (OSGAD)
10-11-2011
Michel Grabisch
Centre d'Économie de la Sorbonne et Université Paris 1-Panthéon Sorbonne, Paris
France
[en] The classical Banzhaf power and interaction indexes used in cooperative game theory appear naturally as leading coefficients in the standard least squares approximation of the game under consideration by a set function of a specified degree. We observe that this still holds true if we consider approximations by set functions depending on specified variables. We show that the Banzhaf influence index can also be obtained from this new approximation problem. Considering certain weighted versions of this approximation, we also introduce a class of weighted Banzhaf influence indexes and analyze their most important properties.
[University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
