Classes of Cooperative Crisp Games
In this chapter we consider three classes of cooperative crisp games: totally balanced games, convex games, and clan games. We introduce basic characterizations of these games and discuss special properties of the set-valued and one-point solution concept
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Rodica Branzei · Dinko Dimitrov · Stef Tijs
Models in Cooperative Game Theory
Second Edition
123
Professor Dr. Rodica Branzei Faculty of Computer Science Alexandru Ioan Cuza University 16 Berthelot St. 700483 Iasi Romania [email protected]
Professor Dr. Stef Tijs CentER and Department of Econometrics and Operations Research Tilburg University 5000 LE Tilburg Netherlands [email protected]
PD Dr. Dinko Dimitrov Chair of Microeconomics Faculty of Law and Economics University of Bayreuth 95440 Bayreuth Germany [email protected]
Originally published as Volume 556 in our Series ‘Lecture Notes in Economics and Mathematical Systems’
ISBN 978-3-540-77953-7
e-ISBN 978-3-540-77954-4
DOI 10.1007/978-3-540-77954-4 Library of Congress Control Number: 2008921947 c 2008, 2005 Springer-Verlag Berlin Heidelberg 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, reuse of illustrations, recitation, broadcasting, reproduction on microfilm 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. Violations are liable to prosecution under the German Copyright Law. 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. Production: le-tex Jelonek, Schmidt & Vöckler GbR, Leipzig Cover-design: WMX Design GmbH, Heidelberg Printed on acid-free paper 987654321 springer.com
Preface
Cooperative game theory is a booming research area with many new developments in the last few years. So, our main purpose when preparing the second edition was to incorporate as much of these new developments as possible without changing the structure of the book. First, this offered us the opportunity to enhance and expand the treatment of traditional cooperative games, called here crisp games, and, especially, that of multi-choice games, in the idea to make the three parts of the monograph more balanced. Second, we have used the opportunity of a second edition to update and enlarge the list of references regarding the three models of cooperative games. Finally, we have benefited from this opportunity by removing typos and a few less important results from the first edition of the book, and by slightly polishing the English style and the punctuation, for the sake of consistency along the monograph. The main changes are: (1) Chapter 3 contains an additional section, Section 3.3, on the average lexicographic value, which is a recent one-point solution concept defined on the class of balanced crisp games. (2) Chapter 4 is new. It offers a brief overview on solution concepts for crisp games from the point of vie
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