Optimal Control Theory with 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 self-contained, it provides an introduction to the use of optimal control theory for deterministic continuous-time 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, state-space 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 control-theoretic concepts to the design of economic mechanisms. Appendixes provide a mathematical review and full solutions to all end-of-chapter problems.
The material is presented at three levels: single-person 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 continuous-time models.
About the Author
Thomas A. Weber is Associate Professor at the Swiss Federal Institute of Technology in Lausanne, Switzerland.
“Weber's book is an important reference for anyone wishing to explore dynamic economic systems. Its early chapters present a nice overview of the field, and for researchers already familiar with control theory there are several chapters dealing with applications to game theory and mechanism design, including interesting examples that are nicely developed.”
—Andrew B. Whinston, Hugh Roy Cullen Centennial Chair in Business Administration and Director of the Center for Research in Electronic Commerce, University of Texas at Austin
“This is an excellent textbook on optimal control theory and its applications to game theory and mechanism design. It will be a valuable resource for economics graduate courses on microeconomics, mathematics for economists, and game theory. Thomas Weber covers his chosen material in depth, clearly, and rigorously. He also offers a mathematical appendix, well-chosen examples, and exercises along with detailed solutions.”
—Dimitrios Diamantaras, Economics Department, Temple University
“This book provides an excellent introduction to optimal control theory and its applications in economics. The exposition is concise and rigorous, with a splendid array of examples from recent research. It is both an outstanding reference on the foundations of optimal control theory and an excellent text for graduate courses dealing with dynamic economic systems.”
—Paul R. Kleindorfer, Anheuser-Busch Professor of Management Science, Emeritus, The Wharton School, University of Pennsylvania, and Distinguished Research Professor, INSEAD
“Thomas Weber's book provides a highly accessible exposition of optimal control theory and games theory, as well as of the techniques of nonlinear analysis on which they are based. A wide constituency of readers, from economics to applied mathematics, engineering and management science, will benefit from its clear exposition, motivational discussion and insights, and a wealth of examples in economics.”
—Richard Vinter, Dean, Faculty of Engineering, Imperial College London