Advances in Dynamic Games and Their Applications Analytical and Nume
This book—an outgrowth of the 12th International Symposium on Dynamic Games—presents current advances in the theory of dynamic games and their applications in several disciplines. The selected contributions cover a variety of topics ranging from purely th
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Series Editor Tamer Bas¸ar
Editorial Board Tamer Bas¸ar, University of Illinois, Urbana Pierre Bernhard, I3S-CNRS and University of Nice-Sophia Antipolis Maurizio Falcone, University of Rome “La Sapienza” Jerzy Filar, University of South Australia, Adelaide Alain Haurie, ORDECSYS, Chˆene-Bougeries, Switzerland Arik A. Melikyan, Russian Academy of Sciences, Moscow Andrzej S. Nowak, Wroclaw University of Technology and University of Zielona G´ora Leon A. Petrosjan, St. Petersburg State University Alain Rapaport, INRIA, Montpelier Josef Shinar, Technion, Haifa
Advances in Dynamic Games and Their Applications Analytical and Numerical Developments
Pierre Bernhard Vladimir Gaitsgory Odile Pourtallier Editors
Birkhäuser Boston • Basel • Berlin
Editors Pierre Bernhard Département de Mathématiques Appliquées et Modélisation Polytech’ Nice-Sophia 930 route des Colles–B.P. 145 06903 Sophia Antipolis Cedex France [email protected]
Vladimir Gaitsgory School of Mathematics and Statistics University of South Australia Mawson Lakes Campus, OC Building Mawson Lakes SA 5095 Australia [email protected]
Odile Pourtallier INRIA–Sophia Antipolis 2004 route des Lucioles–B.P. 93 06902 Sophia Antipolis Cedex France [email protected]
ISBN: 978-0-8176-4833-6 e-ISBN: 978-0-8176-4834-3 DOI: 10.1007/978-0-8176-4834-3 Library of Congress Control Number: 2009921134 Mathematics Subject Classification (2000): 91Axx, 91Bxx, 90Cxx, 49Mxx © Birkhäuser Boston, a part of 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 (Birkhäuser Boston, c/o 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.
Printed on acid-free paper. www.birkhauser.com
Contents
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
PART I
xi
Dynamic-Differential Games: Theoretical Developments
On Differential Games with Long-Time-Average Cost . . . . . . . . . . . . . . . . . . . .
3
Martino Bardi Fields of Extremals and Sufficient Conditions for a Class of Variational Games . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 Dean Carlson Linear Quadratic Differential Games: An Overview . . . . . . . . .
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