Advances in Dynamic Games and Applications PDF
Preview Advances in Dynamic Games and Applications
Annals of the International Society of Dynamic Games Volume 6 Series Editor TamerBaşar Editorial Board Tamer Başar, University of Illinois, Urbana Pierre Bemhard, I3S-CNRS and University of Nice-Sophia Antipolis Maurizio Falcone, University of Roma, "La Sapienza" Jerzy Filar, University of South Australia, Adelaide Alain Haurie, HEC-University of Geneva Arik A. Melikyan, Russian Academy of Sciences, Moscow Andrei Nowak, Technical University of Wroclaw Leo Petrosjan, St. Petersburg State University Alain Rapaport, INRlA, Montpelier Josef Shinar, Technion, Haifa Annals of the International Society of Dynamic Games Advances in Dynamic Games and Applications Eitan Altman Odile Pourtallier Editors Springer Science+Business Media, LLC Eitan Altman Odile Pourtallier INRIA 06902 Sophia Antipolis France Library of Congress CataIoging-in-Publication Data Advances in dynamic games and applications / editors, Eitan Altman, Odile Pourtallier. p. cm.-(Annals of the International Society of Dynamic Games ; 6) Includes bibliographical references. ISBN 978-1-4612-6637-2 ISBN 978-1-4612-0155-7 (eBook) DOI 10.1007/978-1-4612-0155-7 1. Game theory-Congresses. 1. Altman, Eitan. II. Pourtallier, Odile. III. Annals ofthe International Society of Dynamic Games; v. 6. QA269.A364 2001 519.3-dc21 00-069774 AMS Subject Classifications: 91A05, 91A06, 91AlO, 91A15, 91A23, 49N70, 91A25, 91A28, 91A65, 91A80, 49N90, 49N30 Printed on acid-free paper. © 2001 Springer Science+Business Media New York Originally published by Birkhăuser Boston in 2001 Softcover reprint of the hardcover 1s t edition 2001 Copyright is not claimed for works of U .S. Government employees. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without prior permission of the copyright owner. Permission to photocopy for Internal or personal use, or for the internai or personai use of specÎfic clients, is granted by Springer Science+Business Media, LLC for libraries and other users registered with the Copyright Clearance Center (CCC), provided that the base fee of $6.00 per copy, plus $0.20 per page, is paid directly to CCC, 222 Rosewood Drlve, Danvers, MA 01923. USA. Special requests should be addressed directly to Springer Science+Business Media, LLC. ISBN 978-1-4612-6637-2 Production managed by Louise Farkas; manufacturing supervised by Erica Bresler. Typeset by The Bartlett Press, Inc., Marietta, GA. 9 8 765 432 1 Contents Preface ... vii Contributors ix Part I Dynamic Games: Theory On Problems with Information in Some Games: Modelling the Strategies in Some Dynamic Games . . . . . . . . . . . . . . 3 Tadeusz Radzik and A.l. Goldman A Historical Perspective on Cooperative Differential Games 19 Alain Haurie Certainty Equivalence Principle and Minimax Team Problems 31 Pierre Bernhard and Naira Hovakimyan Evolutionary Processes in Signaling Games: The Impact of Different Learning Schemes. . . . . . . . . . . . . . . . . . . . . . . . . . . 45 Gisele Umbhauer Mixed Strategies for Hierarchical Zero-Sum Games 65 Lina Mallozzi and Jacqueline Morgan The Existence and Uniqueness of Equilibria in Convex Games with Strategies in Hilbert Spaces . . . . . . . . . . . . . . . . . . . . . . 79 Dean A. Carlson Part II Stochasic Games The Existence of Equilibrium Payoffs in Two-Player Stochastic Games . . . . . . . . . . . . . . . . . . . 101 Nicolas Vieille Vi Contents Persistently Good Strategies for Nonleavable Stochastic Games with Finite State Space . . . . . . . . . . . . . . . . . . . . . . . . . .. 119 Piercesare Secchi and William D. Sudderth On Stochastic Hybrid Zero-Sum Games with Nonlinear Slow Dynamics . . . . . . . . . . . . . . . . . . . . . . 129 Minh-Tuan Nguyen, Eitan Altman, and Vladimir Gaitsgory On Multichain Markov Games 147 Heinz-Uwe Kiienle Perturbed Zero-Sum Games with Applications to Stochastic and Repeated Games. . . . . . . . . . . . . . . . . . . . . . . . . . 165 Eitan Altman, Eugene A. Feinberg, lerzy Filar, and Vladimir Gaitsgory Part III Solution Methods of Dynamic Games Construction of Singular Surfaces ... 185 Sergey S. Kumkov and Valery S. Patsko Parallel Algorithms for the Isaacs Equation ....... . 203 Maurizio Falcone, Piero Lanucara, and Monica Marinucci Computation of S-adapted Equilibria in Piecewise Deterministic Games via Stochastic Programming Methods .......... 225 Alain Haurie and Francesco Moresino Comparison of Two Numerical Approaches for the Barrier and Value of a Simple Pursuit-Evasion Game . . . . . . . . . . . . . . . . .. 253 Pierre Bernhard, Stephane Crepey, and Alain Rapaport Part IV Dynamic Games: Applications On Optimal Missile Guidance Upgrades with Dynamic Stackelberg Game Linearizations ......................... 277 Michael H. Breitner, Uwe Rettig, and Oskar von Stryk Homicidal Chauffeur Game: Computation of Level Sets of the Value Function ......................... 295 Valery S. Patsko and VL. Turova "The Tragedy of the Commons" Modelled by Large Games . 323 Agnieszka Wiszniewska-Matyszkiel Preface Game theory is a rich and active area of research of which this new volume of the Annals of the International Society of Dynamic Games is yet fresh evidence. Since the second half of the 20th century, the area of dynamic games has man aged to attract outstanding mathematicians, who found exciting open questions requiring tools from a wide variety of mathematical disciplines; economists, so cial and political scientists, who used game theory to model and study competition and cooperative behavior; and engineers, who used games in computer sciences, telecommunications, and other areas. The contents of this volume are primarily based on selected presentation made at the 8th International Symposium of Dynamic Games and Applications, held in Chateau Vaalsbroek, Maastricht, the Netherlands, July 5-8, 1998; this conference took place under the auspices of the International Society of Dynamic Games (ISDG), established in 1990. The conference has been cosponsored by the Control Systems Society of the IEEE, IFAC (International Federation of Automatic Con trol), INRIA (Institute National de Recherche en Informatique et Automatique), and the University of Maastricht. One ofthe activities of the ISDG is the publica tion of the Annals. Every paper that appears in this volume has passed through a stringent reviewing process, as is the case with publications for archival journals. The volume has four parts. The first two parts are theoretic ones: the first (6 papers) on dynamic games (involving deterministic dynamics) and the second (5 papers) on stochastic games. These parts contain mostly novel research results, but also a survey paper on cooperative differential games. The third part of the volume (4 papers) is dedicated to algorithms and numerical solution approaches for dynamic games, and the final part (3 papers) concerns several applications of dynamic games. We wish to thank especially all the associate editors and the referees for their valuable contributions that made this volume possible. Sophia Antipolis, France Eitan Altman Odile Pourtallier Contributors Eitan Altman, INRIA, 2004 Route des lucioles, BP93, 06902 Sophia Antipolis, France Pierre Bernhard, I3S CNRS-UNSA, 200 Route des lucioles, BP12l, 06902 Sophia Antipolis, France Michael H. Breitner, Technische Universitat Clausthal, Fachbereich Mathematik und Informatik, ErzstraBe 1, D-38678 Clausthal-Zellerfeld, Germany Dean A. Carlson, Department of Mathematics, University of Toledo, Toledo, OH 43606-3390, USA Stephane Crepey, INRIA BP 93, 2004 Route des Lucioles, 06902 Sophia-Antipolis Cedex, France Maurizio Falcone, Department of Mathematics, University of Rome, "La Sapienza," P. Aldo Moro 2, 00185 Rome, Italy Eugene A. Feinberg, Department of Applied Mathematics, SUNY at Stony Brook, Stony Brook, NY 11794-3600, USA lerzy Filar, School of Mathematics, University of South Australia, The Levels 5095, Australia Vladimir Gaitsgory, School of Mathematics, University of South Australia, The Levels 5095, Australia Alan l. Goldman, Department of Mathematical Sciences, The John Hopkins University, Baltimore, MD 21218-2682, USA Alain Haurie, LOGILABIHEC, University of Geneva, 102 Boulevard Carl-Vogt, CH-1211, Geneva-4, Switzerland Naira Hovakimyan, Institute of Mechanics, National Academy of Sciences of Armenia, Yerevan, Armenia x Contributors Heinz-Uwe Kilenle, Institut fur Mathematik, Brandenburgische Technische Universistat Cottbus, Postfach 10 13 44, 03013 Cottbus, Germany Sergey S. Kumkov, Institute of Mathematics and Mechanics, Ural Branch of RAS, S. Kovalevskaya Str. 16, Ekaterinburg 620219, Russia Peiro Lanucara, Department of Mathematics, University of Rome "La Sapienza," P. Aldo Moro 2, 00185 Rome, Italy Lina Mallozzi, Dipartimento di Matemaatica e Applicazioni, Universita degli Studi di Napoli "Federico II," Via Claudio 21,80125 Napoli, Italy Monica Marinucci, CASPUR, P. Aldo Moro 2, 00185 Rome, Italy Francesco Moresino, LOGILABIHEC, University of Geneva, 102 Boulevard Carl-Vogt, CH-1211, Geneva-4, Switzerland Jacqueline Morgan, Dipartimento di Matematica e Applicazioni, Universita degli Studi di Napoli "Federico II," Via Claudio 21, 80125 Napoli, Italy Minh-Tuan Nguyen, DSTO, P.O. Box 15000, Salisbury, Australia Valery S. Patsko, Institute of Mathematics and Mechanics, Ural Branch of RAS, S. Kovalevskaya Str. 16, Ekaterinburg 620219, Russia Tadeusz Radzik, Technical University, Institute of Mathematics, Wybreze Wyspianskiego 27, 50-370 Wroc1aw, Poland Alain Rapaport, INRIA, 2 Place Viola, 34060 Montpelier Cedex, France Uwe Rettig, Technische Universitat Munchen, Zentrum Mathematik, D-80290 Munchen, Germany Piercesare Secchi, Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 1-20133 Milano, Italy William D. Sudderth, School of Statistics, University of Minnesota, Minneapolis, MN 55455-0488, USA v.L. Turova, Center of Advanced European Studies and Research, Friedensplatz 16,53111 Bonn, Germany Gisele Umbhauer, Bureau d'Economie Theorique et Appliquee, 62 Avenue de la Foret Noire, 67085 Strasbourg Cedex, France Contributors xi Nicolas Vieille, HEC, Departement Finance et Economie, 78351 Jouy en Josas, France Oskar von Stryk, Technische Universitat Miinchen, Zentrum Mathematik, D-80290 Miinchen, Germany Agnieszka Wisniewska-Matyszkeil, Institute of Applied Mathematics and Mechanics, Warsaw University, 02-097 Warsaw, Poland
The list of books you might like
