Optimal Control Theory with Applications in Economics

This book bridges optimal control theory and economics, discussingordinary differential equations, optimal control, game theory, and mechanism designin one volume. Technically rigorous and largely self-contained, it provides anintroduction to the use of optimal control theory for deterministic continuous-timesystems in economics. The theory of ordinary differential equations (ODEs) is thebackbone of the theory developed in the book, and chapter 2 offers a detailed reviewof basic concepts in the theory of ODEs, including the solution of systems of linearODEs, state-space analysis, potential functions, and stability analysis. Followingthis, the book covers the main results of optimal control theory, in particularnecessary and sufficient optimality conditions; game theory, with an emphasis ondifferential games; and the application of control-theoretic concepts to the designof economic mechanisms. Appendixes provide a mathematical review and full solutionsto all end-of-chapter problems. The material is presented at three levels: single-person decision making; games, in which a group of decision makers interactstrategically; and mechanism design, which is concerned with a designer’s creationof 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. Itis intended for use as a textbook or reference for graduate students, teachers, andresearchers interested in applications of control theory beyond its classical use ineconomic growth. The book will also appeal to readers interested in a modelingapproach to certain practical problems involving dynamic continuous-timemodels.