Differential Games: A Concise Introduction

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.