[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.
Disciplines :
Mathématiques Méthodes quantitatives en économie & gestion
Auteur, co-auteur :
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
Langue du document :
Anglais
Titre :
Influence and interaction indexes in cooperative games: a unified least squares approach
Date de publication/diffusion :
10 novembre 2011
Nom de la manifestation :
5th seminar “Ordered Structures in Games And Decision” (OSGAD)
Organisateur de la manifestation :
Michel Grabisch
Lieu de la manifestation :
Centre d'Économie de la Sorbonne et Université Paris 1-Panthéon Sorbonne, Paris, France
