Models in Cooperative Game Theory Crisp, Fuzzy, and Multi-Choice Gam
This book investigates the classical model of cooperative games with transfer able utility (TU-games) and models in which the players have the possibility to cooperate partially, namely fuzzy and multichoice games. In a crisp game the agents are either f
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Rodica Branzei Dinko Dimitrov StefTijs
Models in Cooperative Game Theory Crisp, Fuzzy, and Multi-Choice Games
Springer
Authors Professor Dr. Rodica Branzei Alexandru loan Cuza University Faculty of Computer Science 16 Berthelot St. 700483 lasi Romania
Dr. Dinko Dimitrov University of Bielefeld UniversitatsstraBe 25 33615 Bielefeld Germany
Professor Dr. StefTijs Faculty of Economics and Business Administration Tilburg University Warandelaan 2 5000 LE Tilburg The Netherlands
Library of Congress Control Number: 2005928812
ISSN 0075-8442 ISBN-10 3-540-26082-X Springer Berlin Heidelberg New York ISBN-13 978-3-540-26082-0 Springer Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9,1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media springeronline. com © Springer-Verlag Berlin Heidelberg 2005 Printed in Germany The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting: Camera ready by author Cover design: Erich Kirchner, Heidelberg Printed on acid-free paper
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Preface
This book investigates the classical model of cooperative games with transferable utility (TU-games) and models in which the players have the possibility to cooperate partially, namely fuzzy and multichoice games. In a crisp game the agents are either fully involved or not involved at all in cooperation with some other agents, while in a fuzzy game players are allowed to cooperate with infinitely many different participation levels, varying from non-cooperation to full cooperation. A multichoice game describes an intermediate case in which each player may have a fixed number of activity levels. Part I of the book is devoted to the most developed model in the theory of cooperative games, that of a classical TU-game with crisp coalitions, which we refer to as crisp game along the book. It presents basic notions, solutions concepts and classes of cooperative crisp games in such a way that allows the reader to use this part as a reference toolbox when studying the corresponding concepts from the theory of fuzzy games (Part II) and from the theory of multichoice games (Part III). The work on this book started while we were research fellows at ZiF (Bielefeld) for the project "Procedural Approaches to Conflict Resolution", 2002. We thank our hosts Ma
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