Paper published in a book (Scientific congresses, symposiums and conference proceedings)
Equivalent representations of a set function with applications to game theory and multicriteria decision making
Grabisch, Michel; MARICHAL, Jean-Luc; Roubens, Marc
1999 • In de Swart, Harrie (Ed.) Proc. of the Int. Conf. on Logic, Game theory and Social choice (LGS'99), Oisterwijk, the Netherlands, May 13-16, 1999
set functions; pseudo-Boolean functions; Möbius inversion formula; Shapley and Banzhaf values; interaction indices; game theory; multicriteria decision making
Abstract :
[en] This paper introduces four alternative representations of a set function: the M¨obius transformation, the co-M¨obius transformation, and the interactions between elements of any subset of a given set as extensions of Shapley and Banzhaf values. The links between the five equivalent representations of a set function are emphasized in this presentation.
Disciplines :
Mathematics Quantitative methods in economics & management
Author, co-author :
Grabisch, Michel; Thomson-CSF, Orsay Cedex, France > Corporate Research Laboratory
MARICHAL, Jean-Luc ; University of Liège, Belgium > Department of Management (FEGSS)
Roubens, Marc; University of Liège, Belgium > Institute of Mathematics
Language :
English
Title :
Equivalent representations of a set function with applications to game theory and multicriteria decision making
Publication date :
May 1999
Event name :
Int. Conf. on Logic, Game theory and Social choice (LGS'99)
Event place :
Oisterwijk, Netherlands
Event date :
from 13-05-1999 to 16-05-1999
Audience :
International
Main work title :
Proc. of the Int. Conf. on Logic, Game theory and Social choice (LGS'99), Oisterwijk, the Netherlands, May 13-16, 1999
