Optimal Control Theory with Applications in Economics  
Thomas A. Weber
The MIT Press
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.