Advances in Dynamic Games Applications to Economics, Management Scie

The paradigms of dynamic games play an important role in the development of multi-agent models in engineering, economics, and management science. The applicability of their concepts stems from the ability to encompass situations with uncertainty, incomple

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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 Roma “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

Annals of the International Society of Dynamic Games

Advances in Dynamic Games Applications to Economics, Management Science, Engineering, and Environmental Management

Alain Haurie Shigeo Muto Leon A. Petrosjan T.E.S. Raghavan Editors

Birkh¨auser Boston • Basel • Berlin

Alain Haurie ORDECSYS Place de l’Etrier 4 Chˆene-Bougeries CH-1224 Switzerland

Shigeo Muto Tokyo Institute of Technology Graduate School of Decision Science and Technology 2-12-1 Ookayama Tokyo 152-8552 Japan

Leon A. Petrosjan State University of St. Petersburg Faculty of Applied Mathematics and Control Processes 198504 St. Petersburg Russia

T.E.S. Raghavan University of Illinois at Chicago Department of Mathematics, Statistics, and Computer Science Chicago, IL 60607-7045 USA

Mathematics Subject Classification: 49N70, 49N75, 49N90, 91-XX, 91Axx, 91A05, 91A06, 91A10, 91A12, 91A13, 91A15, 91A18, 91A20, 91A22, 91A23, 91A24, 91A25, 91A30, 91A35, 91A40, 91A43, 91A44, 91A46, 91A50, 91A55, 91A60, 91A65, 91A60, 91A80 Library of Congress Control Number: 2006924926 ISBN-10 0-8176-4500-4 ISBN-13 978-0-8176-4500-7

e-ISBN: 0-8176-4501-2

Printed on acid-free paper. c 2006 Birkh¨auser Boston 

All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Birkh¨auser 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 in the United States of America. 987654321 www.birkhauser.com

(TXQ/EB)

Contents

Preface

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Contributors

Part I

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ix xvii

Zero-Sum Game Theory

Stochastic Games with Imperfect Monitoring . . . . . . . . . . . . . . . . . . . . . . . . . Dinah Rosenberg, Eilon Solan, and Nicolas Vieille

3

Level Sweeping of the Value Function in Linear Differential Games . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sergey S.