Search Games and Other Applications of Game Theory

This book is on applications of game theory. The title of this book is not "Game Theory and its Applications" because it does not construct a general theory for considered games. The book contains a lot of examples of applica­ tion of game theory together

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Editorial Board: A. Drexl, G. Feichtinger, W Giith, P. Korhonen, U. Schittko, P. Schonfeld, R. Selten Managing Editors: Prof. Dr. G. Fandel Fachbereich Wirtschaftswissenschaften Femuniversitat Hagen Feithstr. 140/AVZ 11,58084 Hagen, Germany Prof. Dr. W. Trockel Institut fUr Mathematische Wirtschaftsforschung (IMW) Universitat Bielefeld Universitatsstr. 25, 33615 Bielefeld, Germany

485

Springer-Verlag Berlin Heidelberg GmbH

Andrey Garnaev

Search Games and Other Applications of Game Theory

Springer

Author Prof. Andrey Gamaev Saint Petersburg State University of Architecture and Civil Engineering Department of Computational Mathematics 2-ya Krasnoarmejskaya 4 Saint Petersburg 198005, Russia

Cataloging-in-Publication Data applied for Die Deutsche Bibliothek - CIP-Einheitsaufnahme Gamaev, Andrej: Search games and other applications of game theory I Andrej Gamaev. - Berlin; Heidelberg ; New York; Barcelona ; Hong Kong ; London ; Paris; Tokyo; Barcelona ; Budapest : Springer, 2000 (Lecture notes in economics and mathematical systems ; 485)

ISBN 978-3-540-67195-4

ISSN 0075-8442 ISBN 978-3-540-67195-4 DOI 10.1007/978-3-642-57304-0

ISBN 978-3-642-57304-0 (eBook)

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© Springer-Verlag Berlin Heidelberg 2000 Originally published by Springer-Verlag Berlin Heidelberg New York in 2000 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. Typesetting: Camera ready by author Printed on acid-free paper SPIN: 10734512

42/3143/du-543210

Preface

This book is on applications of game theory. The title of this book is not "Game Theory and its Applications" because it does not construct a general theory for considered games. The book contains a lot of examples of application of game theory together with the background of those games considered and a list of unsolved problems. Also we consider only the game where the optimal strategies of the players are found in closed form. This book is an attempt to carryon the approach developed in nice books "Search Games" by Gal and "Geometric Games and their Applications" by Ruckle. The first chapter of this book supplies the required definitions and theorems from game theory. The second chapter deals with discrete search