[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 :
Mathematics Quantitative methods in economics & management
Author, co-author :
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
Language :
English
Title :
Influence and interaction indexes in cooperative games: a unified least squares approach
Publication date :
10 November 2011
Event name :
5th seminar “Ordered Structures in Games And Decision” (OSGAD)
Event organizer :
Michel Grabisch
Event place :
Centre d'Économie de la Sorbonne et Université Paris 1-Panthéon Sorbonne, Paris, France