Cooperative Stochastic Differential Games

ISBN-13: 9780387276205 / Angielski / Twarda / 2005 / 260 str.

David W. K. Yeung; Leon A. Petrosyan

Opis

Stochastic differential games represent one of the most complex forms of decision making under uncertainty. In particular, interactions between strategic behaviors, dynamic evolution and stochastic elements have to be considered simultaneously. The complexity of stochastic differential games generally leads to great difficulties in the derivation of solutions. Cooperative games hold out the promise of more socially optimal and group efficient solutions to problems involving strategic actions. Despite urgent calls for national and international cooperation, the absence of formal solutions has precluded rigorous analysis of this problem. The book supplies effective tools for rigorous study of cooperative stochastic differential games. In particular, a generalized theorem for the derivation of analytically tractable "payoff distribution procedure" of subgame consistent solution is presented. Being capable of deriving analytical tractable solutions, the work is not only theoretically interesting but would enable the hitherto intractable problems in cooperative stochastic differential games to be fruitfully explored. Currently, this book is the first ever volume devoted to cooperative stochastic differential games. It aims to provide its readers an effective tool to analyze cooperative arrangements of conflict situations with uncertainty over time. Cooperative game theory has succeeded in offering many applications of game theory in operations research, management, economics, politics and other disciplines. The extension of these applications to a dynamic environment with stochastic elements should be fruitful. The book will be of interest to game theorists, mathematicians, economists, policy-makers, corporate planners and graduate students.

Recenzje

From the reviews:

"This book is written by two of the main experts in the theory of cooperative stochastic differential games. It includes the results of many recent articles in the field, mainly by the authors themselves. ... In fact there is no other textbook on cooperative stochastic differential games and this makes the book a must for everyone interested ... . The book is nicely written and reads well ... ." (Christian-Oliver Ewald, Mathematical Reviews, Issue 2006 i)

"This book is concerned with the study of cooperative stochastic differential games and applications (mainly to economics and management sciences). ... There is a real core throughout this monography to link the theory with application. This work is one of the first books studying cooperative stochastic differential games. It is very well-written in a very comprehensive manner. This will attract the attention of scientists who work on game theory but also of people using the theory of games." (Marc Quincampoix, Zentralblatt MATH, Vol. 1108 (10), 2007)

"This interesting book aims at the synthesis of two major branches of game theory: the cooperative and differential games. ... The style is rigorous and, derivations of important formulae are presented in a detailed way. ... Overall, this is an important new book on an important-still emerging-topic. I am happy to recommend it to all serious game theory students and researchers as it is likely to stimulate a lot of further developments." (Jerzy A. Filar, SIAM Review, Vol. 49 (3), 2007)

Spis treści

Deterministic and Stochastic Differential Games.- Cooperative Differential Games in Characteristic Function Form.- Two-person Cooperative Differential Games with Discounting.- Two-person Cooperative Stochastic Differential Games.- Multiplayer Cooperative Stochastic Differential Games.- Cooperative Stochastic Differential Games with Nontransferable Payoffs.

O autorze

Prof. Dr. Dr.h.c. David W. K. Yeung is Distinguished Research Professor and Head of Business Administration at Hong Kong Shue Yan University, and Kantorovich Research Chair in Stochastic Differential Games and Co-director of Centre of Game Theory at Saint Petersburg State University. He is also Distinguished Honorary Professor of Qingdao University - an honor he received along with Nobel laureates John Nash, Reinhard Selten and Robert Aumann. Yeung's main areas of research are game theory, optimization and stochastic processes. He serves as Managing Editor of International Game Theory Review, Guest Editor of Annals of Operations Research, Associate Editor of Dynamic Games & Applications and Editorial Board Member of Mathematical Game Theory & Applications. Yeung has published extensively in world renowned science journals, in particular, Automatica, Journal of Optimization Theory and Applications, Annals of Operations Research, European Journal of Operational Research, International Game Theory Review and Mathematical Biosciences.

Blurb

Numerical Optimization presents a comprehensive and up-to-date description of the most effective methods in continuous optimization. It responds to the growing interest in optimization in engineering, science, and business by focusing on the methods that are best suited to practical problems.

For this new edition the book has been thoroughly updated throughout. There are new chapters on nonlinear interior methods and derivative-free methods for optimization, both of which are used widely in practice and the focus of much current research. Because of the emphasis on practical methods, as well as the extensive illustrations and exercises, the book is accessible to a wide audience. It can be used as a graduate text in engineering, operations research, mathematics, computer science, and business. It also serves as a handbook for researchers and practitioners in the field. The authors have strived to produce a text that is pleasant to read, informative, and rigorous - one that reveals both the beautiful nature of the discipline and its practical side.