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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

Author : Jiongmin Yong
ISBN : 9814596221
Genre : Business & Economics
File Size : 41.45 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.

Author : Wendell H. Fleming
ISBN : 9780387310718
Genre : Mathematics
File Size : 37.45 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.

Author : David A. Blackwell
ISBN : 9780486638317
Genre : Mathematics
File Size : 55.86 MB
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A problem-oriented text for evaluating statistical procedures through decision and game theory. First-year graduates in statistics, computer experts and others will find this highly respected work best introduction to growing field.

Author : R. Duncan Luce
ISBN : 9780486134833
Genre : Mathematics
File Size : 75.5 MB
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Superb non-technical introduction to game theory, primarily applied to social sciences. Clear, comprehensive coverage of utility theory, 2-person zero-sum games, 2-person non-zero-sum games, n-person games, individual and group decision-making, more. Bibliography.

Author : John D. Beasley
ISBN : 9780486151625
Genre : Mathematics
File Size : 83.68 MB
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Lucid, instructive, and full of surprises, this book examines how simple mathematical analysis can throw unexpected light on games of every type, from poker to golf to the Rubik's cube. 1989 edition.

Author : Steven Vajda
ISBN : NWU:35556037906062
Genre : Mathematics
File Size : 89.8 MB
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This refreshingly authoritative look at recreational mathematics illustrates winning strategies that use the methods of algebra, geometry, combinatorics, number theory, graph theory, and other branches of mathematics. Its lucid analyses of the rules and theories of mathematical games include skill-enhancing exercises, plus references, appendixes, and detailed explanations. 1992 edition.

Author : T. J. Willmore
ISBN : 9780486282107
Genre : Mathematics
File Size : 41.22 MB
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This text employs vector methods to explore the classical theory of curves and surfaces. Topics include basic theory of tensor algebra, tensor calculus, calculus of differential forms, and elements of Riemannian geometry. 1959 edition.

Author : E. C. Zachmanoglou
ISBN : 9780486132174
Genre : Mathematics
File Size : 73.6 MB
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This text explores the essentials of partial differential equations as applied to engineering and the physical sciences. Discusses ordinary differential equations, integral curves and surfaces of vector fields, the Cauchy-Kovalevsky theory, more. Problems and answers.