Cooperative and Noncooperative Multi-Level Programming
This addition to the OPERATIONS RESEARCH/COMPUTER SCIENCE INTERFACES Series represents a sorely-needed advance in decision science and game theory literature. Drs. Sakawa and Nishizaki present their combined work in applying both cooperative and noncooper
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Masatoshi Sakawa • Ichiro Nishizaki
Cooperative and Noncooperative Multi-Level Programming
Masatoshi Sakawa Department of Artificial Complex Systems Engineering Hiroshima University 1-4-1 Kagamiyama Higashi-Hiroshima 739-8527 Japan [email protected]
Ichiro Nishizaki Department of Artificial Complex Systems Engineering Hiroshima University 1-4-1 Kagamiyama Higashi-Hiroshima 739-8527 Japan [email protected]
ISSN 1387-666X ISBN 978-1-4419-0675-5 e-ISBN 978-1-4419-0676-2 DOI 10.1007/978-1-4419-0676-2 Springer Dordrecht Heidelberg London New York Library of Congress Control Number: 2009926796 © Springer Science+Business Media, LLC 2009 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights.
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Preface
To derive rational and convincible solutions to practical decision making problems in complex and hierarchical human organizations, the decision making problems are formulated as relevant mathematical programming problems which are solved by developing optimization techniques so as to exploit characteristics or structural features of the formulated problems. In particular, for resolving conflict in decision making in hierarchical managerial or public organizations, the multi-level formulation of the mathematical programming problems has been often employed together with the solution concept of Stackelberg equilibrium. However, we conceive that a pair of the conventional formulation and the solution concept is not always sufficient to cope with a large variety of decision making situations in actual hierarchical organizations. The following issues should be taken into consideration in expression and formulation of decision making problems. In formulation of mathematical programming problems, it is tacitly supposed that decisions are made by a single person while game theory deals with economic behavior of multiple decision makers with fully rational judgment. Because two-level mathematical programming problems are interpreted as static Stackelberg games, multi-level mathematical programming is relevant to noncooperative game theory; in conventional multi-level mathematical programming models employing the solution concept of Stackelberg equilibrium, it is assumed that there is no communication among decision makers,
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