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This volume lays the mathematical foundations for the theory of differential games, developing a rigorous mathematical framework with existence theorems. It begins with a precise definition of a differential game and advances to considerations of games of fixed duration, games of pursuit and evasion, the computation of saddle points, games of survival, and games with restricted phase coordinates. Final chapters cover selected topics (including capturability and games with delayed information) and N-person games.Geared toward graduate students, Differential Games will be of particular interest to professionals in the fields of electrical engineering, industrial engineering, economics, and mathematics. Although intended primarily for self-study, it can be used as a core or ancillary text in courses in differential games, game theory, and control theory.
To be very straightforward, this is not a book for beginners. And it doesn't claim to be. This book assumes a good understanding of not only the computational aspects of differential equations, but also of the the theoretical.Friedman's Differential Games offers a very good, rigorous framework for Differential Game Theory. Unfortunately, that same rigor makes it difficult to approach, and hard to learn. Expect to take a lot of time working the problems, and consider leaving this book until after reading a more basic text, like Issacs' Differential Games.