Cooperative Stochastic Differential Games
Cooperative Stochastic Differential Games

Author: David W.K. Yeung

Publisher: Springer Science & Business Media

Published: 2006-05-11

Total Pages: 253

ISBN-13: 038727622X

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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.

Differential Games in Economics and Management Science
Differential Games in Economics and Management Science

Author: Engelbert Dockner

Publisher: Cambridge University Press

Published: 2000-11-16

Total Pages: 398

ISBN-13: 9780521637329

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A comprehensive, self-contained survey of the theory and applications of differential games, one of the most commonly used tools for modelling and analysing economics and management problems which are characterised by both multiperiod and strategic decision making. Although no prior knowledge of game theory is required, a basic knowledge of linear algebra, ordinary differential equations, mathematical programming and probability theory is necessary. Part One presents the theory of differential games, starting with the basic concepts of game theory and going on to cover control theoretic models, Markovian equilibria with simultaneous play, differential games with hierarchical play, trigger strategy equilibria, differential games with special structures, and stochastic differential games. Part Two offers applications to capital accumulation games, industrial organization and oligopoly games, marketing, resources and environmental economics.

Non-cooperative Stochastic Differential Game Theory of Generalized Markov Jump Linear Systems
Non-cooperative Stochastic Differential Game Theory of Generalized Markov Jump Linear Systems

Author: Cheng-ke Zhang

Publisher: Springer

Published: 2016-09-02

Total Pages: 196

ISBN-13: 331940587X

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This book systematically studies the stochastic non-cooperative differential game theory of generalized linear Markov jump systems and its application in the field of finance and insurance. The book is an in-depth research book of the continuous time and discrete time linear quadratic stochastic differential game, in order to establish a relatively complete framework of dynamic non-cooperative differential game theory. It uses the method of dynamic programming principle and Riccati equation, and derives it into all kinds of existence conditions and calculating method of the equilibrium strategies of dynamic non-cooperative differential game. Based on the game theory method, this book studies the corresponding robust control problem, especially the existence condition and design method of the optimal robust control strategy. The book discusses the theoretical results and its applications in the risk control, option pricing, and the optimal investment problem in the field of finance and insurance, enriching the achievements of differential game research. This book can be used as a reference book for non-cooperative differential game study, for graduate students majored in economic management, science and engineering of institutions of higher learning.

LQ Dynamic Optimization and Differential Games
LQ Dynamic Optimization and Differential Games

Author: Jacob Engwerda

Publisher: John Wiley & Sons

Published: 2005-06-17

Total Pages: 514

ISBN-13: 9780470015247

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Game theory is the theory of social situations, and the majority of research into the topic focuses on how groups of people interact by developing formulas and algorithms to identify optimal strategies and to predict the outcome of interactions. Only fifty years old, it has already revolutionized economics and finance, and is spreading rapidly to a wide variety of fields. LQ Dynamic Optimization and Differential Games is an assessment of the state of the art in its field and the first modern book on linear-quadratic game theory, one of the most commonly used tools for modelling and analysing strategic decision making problems in economics and management. Linear quadratic dynamic models have a long tradition in economics, operations research and control engineering; and the author begins by describing the one-decision maker LQ dynamic optimization problem before introducing LQ differential games. Covers cooperative and non-cooperative scenarios, and treats the standard information structures (open-loop and feedback). Includes real-life economic examples to illustrate theoretical concepts and results. Presents problem formulations and sound mathematical problem analysis. Includes exercises and solutions, enabling use for self-study or as a course text. Supported by a website featuring solutions to exercises, further examples and computer code for numerical examples. LQ Dynamic Optimization and Differential Games offers a comprehensive introduction to the theory and practice of this extensively used class of economic models, and will appeal to applied mathematicians and econometricians as well as researchers and senior undergraduate/graduate students in economics, mathematics, engineering and management science.

Stochastic Game Strategies and their Applications
Stochastic Game Strategies and their Applications

Author: Bor-Sen Chen

Publisher: CRC Press

Published: 2019-07-31

Total Pages: 600

ISBN-13: 0429780516

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Game theory involves multi-person decision making and differential dynamic game theory has been widely applied to n-person decision making problems, which are stimulated by a vast number of applications. This book addresses the gap to discuss general stochastic n-person noncooperative and cooperative game theory with wide applications to control systems, signal processing systems, communication systems, managements, financial systems, and biological systems. H∞ game strategy, n-person cooperative and noncooperative game strategy are discussed for linear and nonlinear stochastic systems along with some computational algorithms developed to efficiently solve these game strategies.

Stochastic Differential Games. Theory and Applications
Stochastic Differential Games. Theory and Applications

Author: Kandethody M. Ramachandran

Publisher: Springer Science & Business Media

Published: 2012-01-05

Total Pages: 253

ISBN-13: 9491216473

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The subject theory is important in finance, economics, investment strategies, health sciences, environment, industrial engineering, etc.

Optimal Control Theory
Optimal Control Theory

Author: Suresh P. Sethi

Publisher: Taylor & Francis US

Published: 2006

Total Pages: 536

ISBN-13: 9780387280929

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Optimal control methods are used to determine optimal ways to control a dynamic system. The theoretical work in this field serves as a foundation for the book, which the authors have applied to business management problems developed from their research and classroom instruction. Sethi and Thompson have provided management science and economics communities with a thoroughly revised edition of their classic text on Optimal Control Theory. The new edition has been completely refined with careful attention to the text and graphic material presentation. Chapters cover a range of topics including finance, production and inventory problems, marketing problems, machine maintenance and replacement, problems of optimal consumption of natural resources, and applications of control theory to economics. The book contains new results that were not available when the first edition was published, as well as an expansion of the material on stochastic optimal control theory.

Stochastic Dynamics
Stochastic Dynamics

Author: Hans Crauel

Publisher: Springer Science & Business Media

Published: 2007-12-14

Total Pages: 457

ISBN-13: 0387226559

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Focusing on the mathematical description of stochastic dynamics in discrete as well as in continuous time, this book investigates such dynamical phenomena as perturbations, bifurcations and chaos. It also introduces new ideas for the exploration of infinite dimensional systems, in particular stochastic partial differential equations. Example applications are presented from biology, chemistry and engineering, while describing numerical treatments of stochastic systems.

Subgame Consistent Cooperation
Subgame Consistent Cooperation

Author: David W.K. Yeung

Publisher: Springer

Published: 2016-09-23

Total Pages: 522

ISBN-13: 9811015457

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Strategic behavior in the human and social world has been increasingly recognized in theory and practice. It is well known that non-cooperative behavior could lead to suboptimal or even highly undesirable outcomes. Cooperation suggests the possibility of obtaining socially optimal solutions and the calls for cooperation are prevalent in real-life problems. Dynamic cooperation cannot be sustainable if there is no guarantee that the agreed upon optimality principle at the beginning is maintained throughout the cooperation duration. It is due to the lack of this kind of guarantees that cooperative schemes fail to last till its end or even fail to get started. The property of subgame consistency in cooperative dynamic games and the corresponding solution mechanism resolve this “classic” problem in game theory. This book is a comprehensive treatise on subgame consistent dynamic cooperation covering the up-to-date state of the art analyses in this important topic. It sets out to provide the theory, solution techniques and applications of subgame consistent cooperation in a wide spectrum of paradigms for analysis which includes cooperative dynamic game models with stochastic state dynamics, with uncertain future payoffs, with asynchronous players’ horizons, with random cooperation duration, with control spaces switching and with transferable and nontransferable payoffs. The book would be a significant research reference text for researchers in game theory, economists, applied mathematicians, policy-makers, corporate decision-makers, and graduate students in applied mathematics, game theory, decision sciences, economics and management sciences.

Differential Games and Applications
Differential Games and Applications

Author: Tamer S. Basar

Publisher: Springer

Published: 2014-03-12

Total Pages: 205

ISBN-13: 9783662168660

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This volume contains fifteen articles on the topic of differential and dynamic games, focusing on both theory and applications. It covers a variety of areas and presents recent developments on topics of current interest. It should be useful to researchers in differential and dynamic games, systems and control, operations research and mathematical economics.