differential games a concise introduction

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Differential Games

Author : Jiongmin Yong
ISBN : 9789814596244
Genre : Mathematics
File Size : 85. 87 MB
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This book uses a small volume to present the most basic results for deterministic two-person differential games. The presentation begins with optimization of a single function, followed by a basic theory for two-person games. For dynamic situations, the author first recalls control theory which is treated as single-person differential games. Then a systematic theory of two-person differential games is concisely presented, including evasion and pursuit problems, zero-sum problems and LQ differential games. The book is intended to be self-contained, assuming that the readers have basic knowledge of calculus, linear algebra, and elementary ordinary differential equations. The readership of the book could be junior/senior undergraduate and graduate students with majors related to applied mathematics, who are interested in differential games. Researchers in some other related areas, such as engineering, social science, etc. will also find the book useful. Contents:IntroductionControl Theory — Single-Player Differential GamesTwo-Person Zero Sum Differential Games — A General ConsiderationDifferential Games with Unbounded ControlsDifferential Games of Pursuit and EvasionLinear-Quadratic Differential GamesDifferential Games with Switching Strategies Readership: Researchers in optimization and control theory and also game theory and economics. The book will be a supplementary volume to relevant textbooks and/or a good research reference book in certain areas. Keywords:Two-Person Differential Games;Zero-Sum;Evasion;Pursuit;Elliot-Kalton Strategy;Hamilton-Jacobi Equation;Viscosity Solution;Optimal Control;Viability;Controllability;Linear-Quadratic Problem;Switching and Impulse Control

Differential Games

Author : Jiongmin Yong
ISBN : 9814596221
Genre : Business & Economics
File Size : 21. 7 MB
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This book uses a small volume to present the most basic results for deterministic two-person differential games. The presentation begins with optimization of a single function, followed by a basic theory for two-person games. For dynamic situations, the author first recalls control theory which is treated as single-person differential games. Then a systematic theory of two-person differential games is concisely presented, including evasion and pursuit problems, zero-sum problems and LQ differential games. The book is intended to be self-contained, assuming that the readers have basic knowledge of calculus, linear algebra, and elementary ordinary differential equations. The readership of the book could be junior/senior undergraduate and graduate students with majors related to applied mathematics, who are interested in differential games. Researchers in some other related areas, such as engineering, social science, etc. will also find the book useful.

Understanding Game Theory

Author : Vassili N Kolokoltsov
ISBN : 9789813107748
Genre :
File Size : 39. 26 MB
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Steadily growing applications of game theory in modern science (including psychology, biology and economics) require sources to provide rapid access in both classical tools and recent developments to readers with diverse backgrounds. This book on game theory, its applications and mathematical methods, is written with this objective in mind. The book gives a concise but wide-ranging introduction to games including older (pre-game theory) party games and more recent topics like elections and evolutionary games and is generously spiced with excursions into philosophy, history, literature and politics. A distinguished feature is the clear separation of the text into two parts: elementary and advanced, which makes the book ideal for study at various levels. Part I displays basic ideas using no more than four arithmetic operations and requiring from the reader only some inclination to logical thinking. It can be used in a university degree course without any (or minimal) prerequisite in mathematics (say, in economics, business, systems biology), as well as for self-study by school teachers, social and natural scientists, businessmen or laymen. Part II is a rapid introduction to the mathematical methods of game theory, suitable for a mathematics degree course of various levels. It includes an advanced material not yet reflected in standard textbooks, providing links with the exciting modern developments in financial mathematics (rainbow option pricing), tropical mathematics, statistical physics (interacting particles) and discusses structural stability, multi-criteria differential games and turnpikes. To stimulate the mathematical and scientific imagination, graphics by a world-renowned mathematician and mathematics imaging artist, A T Fomenko, are used. The carefully selected works of this artist fit remarkably into the many ideas expressed in the book.

Differential Games

Author : Rufus Isaacs
ISBN : 9780486135984
Genre : Mathematics
File Size : 23. 79 MB
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Definitive work draws on game theory, calculus of variations, and control theory to solve an array of problems: military, pursuit and evasion, athletic contests, many more. Detailed examples, formal calculations. 1965 edition.

Differential Games In Economics And Management Science

Author : Engelbert Dockner
ISBN : 0521637325
Genre : Business & Economics
File Size : 39. 91 MB
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Graduate textbook presenting the theory and applications of differential games, assuming no prior knowledge of game theory.

Differential Games

Author : Avner Friedman
ISBN : 9780486153278
Genre : Mathematics
File Size : 78. 21 MB
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Graduate-level text surveys games of fixed duration, games of pursuit and evasion, the computation of saddle points, games of survival, games with restricted phase coordinates, and N-person games. 1971 edition.

Controlled Markov Processes And Viscosity Solutions

Author : Wendell H. Fleming
ISBN : 9780387310718
Genre : Mathematics
File Size : 62. 11 MB
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This book is an introduction to optimal stochastic control for continuous time Markov processes and the theory of viscosity solutions. It covers dynamic programming for deterministic optimal control problems, as well as to the corresponding theory of viscosity solutions. New chapters in this second edition introduce the role of stochastic optimal control in portfolio optimization and in pricing derivatives in incomplete markets and two-controller, zero-sum differential games.

A Concise Introduction To Calculus

Author : Wu Yi Hsiang
ISBN : 9810219016
Genre : Mathematics
File Size : 33. 27 MB
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The student of calculus is entitled to ask what calculus is and what it can be used for. This short book provides an answer.The author starts by demonstrating that calculus provides a mathematical tool for the quantitative analysis of a wide range of dynamical phenomena and systems with variable quantities.He then looks at the origins and intuitive sources of calculus, its fundamental methodology, and its general framework and basic structure, before examining a few typical applications.The author's style is direct and pedagogical. The new student should find that the book provides a clear and strong grounding in this important technique.

Optimal Control Theory With Applications In Economics

Author : Thomas A. Weber
ISBN : 0262015730
Genre : Business & Economics
File Size : 42. 87 MB
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A rigorous introduction to optimal control theory, with an emphasis on applications in economics. This book bridges optimal control theory and economics, discussing ordinary differential equations, optimal control, game theory, and mechanism design in one volume. Technically rigorous and largely self-contained, it provides an introduction to the use of optimal control theory for deterministic continuous-time systems in economics. The theory of ordinary differential equations (ODEs) is the backbone of the theory developed in the book, and chapter 2 offers a detailed review of basic concepts in the theory of ODEs, including the solution of systems of linear ODEs, state-space analysis, potential functions, and stability analysis. Following this, the book covers the main results of optimal control theory, in particular necessary and sufficient optimality conditions; game theory, with an emphasis on differential games; and the application of control-theoretic concepts to the design of economic mechanisms. Appendixes provide a mathematical review and full solutions to all end-of-chapter problems. The material is presented at three levels: single-person decision making; games, in which a group of decision makers interact strategically; and mechanism design, which is concerned with a designer's creation of an environment in which players interact to maximize the designer's objective. The book focuses on applications; the problems are an integral part of the text. It is intended for use as a textbook or reference for graduate students, teachers, and researchers interested in applications of control theory beyond its classical use in economic growth. The book will also appeal to readers interested in a modeling approach to certain practical problems involving dynamic continuous-time models.

Introduction To Differential Games And Control Theory

Author : V. N. Lagunov
ISBN : UOM:39015015627063
Genre : Differential games
File Size : 69. 88 MB
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