Game theory is a theory of conflict and cooperation between rational decision makers. It relies heavily on mathematical models and has proven useful to address problems of conflict and cooperation in economics and management science, as well as other areas of social science. Differential games are dynamic game models used to study systems that evolve in continuous time and where the system dynamics can be described by differential equations.

This book is a self-contained introduction to differential game theory and its applications in economics and management science. The book is introductory, but not elementary. It requires no prior knowledge of game theory, although to benefit fully from the theoretical developments in chapters 3 to 8, and to understand the various steps of the analysis of the applications in chapters 9 to 12, a basic knowledge of mathematical analysis, linear algebra, ordinary differential equations, mathematical programming, and probability theory is necessary. Whenever appropriate, we provide supporting references in these areas. The applications treated in chapters 9 to 12 presuppose that the reader is familiar with basic concepts in economics and management science. The selection of the topics dealt with in the applications chapters has to some extent been guided by the personal research interests of the authors. Nevertheless, the areas covered in these chapters comprise a fairly large subset of the interesting applications of differential games in economics and management science.