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Optimal Control Theory with Applications in Economics (Mit Press),New
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A rigorous introduction to optimal control theory, with an emphasis on applications in economics.This book bridges optimal control theory and economics, discussing ordinary differential equations, optimal control, game theory, and mechanism design in one volume. Technically rigorous and largely selfcontained, it provides an introduction to the use of optimal control theory for deterministic continuoustime systems in economics. The theory of ordinary differential equations (ODEs) is the backbone of the theory developed in the book, and chapter 2 offers a detailed review of basic concepts in the theory of ODEs, including the solution of systems of linear ODEs, statespace analysis, potential functions, and stability analysis. Following this, the book covers the main results of optimal control theory, in particular necessary and sufficient optimality conditions; game theory, with an emphasis on differential games; and the application of controltheoretic concepts to the design of economic mechanisms. Appendixes provide a mathematical review and full solutions to all endofchapter problems.The material is presented at three levels: singleperson decision making; games, in which a group of decision makers interact strategically; and mechanism design, which is concerned with a designer's creation of an environment in which players interact to maximize the designer's objective. The book focuses on applications; the problems are an integral part of the text. It is intended for use as a textbook or reference for graduate students, teachers, and researchers interested in applications of control theory beyond its classical use in economic growth. The book will also appeal to readers interested in a modeling approach to certain practical problems involving dynamic continuoustime models.
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