cooperative games; interaction among players; values and interaction indices
Abstract :
[en] In the framework of cooperative game theory, the concept of interaction index, which can be regarded as an extension of that of value, has been recently proposed to measure the interaction phenomena among players. Axiomatizations of two classes of interaction indices, namely probabilistic interaction indices and cardinal-probabilistic interaction indices, generalizing probabilistic values and semivalues, respectively, are first proposed. The axioms we utilize are based on natural generalizations of axioms involved in the axiomatizations of values. In the second half of the paper, existing instances of cardinal-probabilistic interaction indices encountered thus far in the literature are also axiomatized.
Disciplines :
Mathematics Quantitative methods in economics & management
Identifiers :
UNILU:UL-ARTICLE-2010-392
Author, co-author :
Fujimoto, Katsushige; Fukushima University, Fukushima, Japan > Faculty of Economics
Kojadinovic, Ivan; École Polytechnique de l’Université de Nantes, Nantes, France > LINA CNRS FRE 2729
Marichal, Jean-Luc ; University of Luxembourg > Faculty of Law, Economics and Finance (FDEF) > Applied Mathematics Unit (SMA)
Language :
English
Title :
Axiomatic characterizations of probabilistic and cardinal-probabilistic interaction indices
Publication date :
April 2006
Journal title :
Games and Economic Behavior
ISSN :
0899-8256
Publisher :
Elsevier
Volume :
55
Issue :
1
Pages :
72-99
Peer reviewed :
Peer reviewed
Name of the research project :
Recherches méthodologiques et mathématiques en aide à la décision et à la classification > 01/01/2005 – 12/12/2007 > BISDORFF Raymond