Discover a comprehensive and rigorous introduction to optimal control theory with a special focus on its applications in economics. This authoritative volume seamlessly bridges the gap between control theory and economic analysis, covering essential topics such as ordinary differential equations, optimal control, game theory, and mechanism design. Designed to be largely self-contained, it offers a thorough foundation for understanding how optimal control techniques can be applied to deterministic continuous-time systems within an economic context.
The backbone of the book is the theory of ordinary differential equations (ODEs). Chapter 2 provides a detailed review of fundamental concepts, including the solution of systems of linear ODEs, state-space analysis, potential functions, and stability analysis. Building on this foundation, the text explores the main results of optimal control theory, emphasizing necessary and sufficient optimality conditions. It also delves into game theory, with particular attention to differential games, and discusses how control-theoretic concepts can be employed in the design of economic mechanisms.
To support the reader’s understanding, the book includes appendices that offer a mathematical review and provide full solutions to all end-of-chapter problems. The material is presented at three distinct levels: single-person decision making, strategic interactions among multiple decision makers through games, and mechanism design, which involves creating environments where players interact to achieve specific objectives. Throughout, the focus remains on practical applications, with problems integrated into the text to reinforce learning.
Intended as both a textbook and a reference, this book is suitable for graduate students, educators, and researchers interested in extending control theory beyond its traditional applications in economic growth. Its modeling approach makes it particularly appealing to those seeking to understand and solve practical problems involving dynamic, continuous-time models in economics and related fields.