Dynamic Optimization and Differential Games

Dynamic Optimization and Differential Games has been written to address the increasing number of Operations Research and Management Science problems that involve the explicit consideration of time and of gaming among multiple agents. With end-of-chapter exercises throughout, it is a book that can be used both as a reference and as a textbook. It will be useful as a guide to engineers, operations researchers, applied mathematicians and social scientists whose work involves both the theoretical and computational aspects of dynamic optimization and differential games. Included throughout the text are detailed explanations of several original dynamic and game-theoretic mathematical models which are of particular relevance in today’s technologically-driven-global economy: revenue management, oligopoly pricing, production planning, supply chain management, dynamic traffic assignment and dynamic congestion pricing.

The book emphasizes deterministic theory, computational tools and applications associated with the study of dynamic optimization and competition in continuous time. It develops the key results of deterministic, continuous time, optimal control theory from both the classical calculus of variations perspective and the more modern approach of infinite dimensional mathematical programming. These results are then generalized for the analysis of differential variational inequalities arising in dynamic game theory for open loop environments. Algorithms covered include steepest descent in Hilbert space, gradient projection in Hilbert space, fixed point methods, and gap function methods.

From the reviews:

“This book contains an introductory chapter and nine other chapters, divided into three parts. … The intended readers are graduate students and researchers interested in modeling and computing in continuous time. … I strongly recommend this book to readers interested in dynamic optimization in continuous time. I found it excellent on many counts, especially its detailed modeling analysis and its computational aspects. … used as a textbook for a one-semester course on mathematical programming and optimal control.” (Georges Zaccour, SIAM Review, Vol. 54 (2), 2012)

“This book is devoted to optimal control and differential game problems with emphasis on economic applications such as revenue management, oligopoly pricing, production planning, supply chain management, and dynamic network problems. The author describes (differential) variational inequalities as basic tool for solving these problems. … The book presentation is given at a student’s level, contains many significant examples and exercises, so that it can be used as a textbook.” (Igor V. Konnov, Zentralblatt MATH, Vol. 1207, 2011)