In this paper, we provide a survey of dynamic game theory with special emphasis on past and possible future applications to problems of international economic policy making, where we will concentrate on macroeconomic and stabilization policy problems. First, the paper gives a brief introduction to the theory of dynamic games as developed mostly by mathematicians and control engineers. Dynamic game theory may be regarded as a predecessor and at the same time a substantial extension of the framework of optimum control theory. Next, we will show that dynamic game theory has already been proved to allow important insights into problems of economics, in particular economic policy. Although the number and quality of studies applying the theory of dynamic games are already impressive, we identify some areas where the potential for using dynamic game theory is still not fully utilized. Strangely, the importance of the analytical tools of dynamic game theory for the theory of economic policy is largely neglected just by economists dealing with some problems and results that have been originally developed by mathematicians and control engineers. The topic of time-inconsistency is a case in point for a successful application of dynamic game theory that - although of enormous influence on the theory and practice of economic policy - went largely unnoticed as a particular application of dynamic game theory by the economics profession. Drawing on the author's research, the paper shows how the theory of dynamic games can be applied to problems of economic policymaking with heterogeneous policy-makers whose behavior is characterized by strategic interactions. In particular, for the case of macroeconomic policy-making in a monetary union, strategic interactions between governments of the union's member countries responsible for national fiscal policies and the common central bank responsible for the union's monetary policy can be studied in a fruitful way, using concepts and results from dynamic game theory as applied to a macroeconomic model. It is investigated how policies with and without self-commitment on the one hand and non-cooperative and cooperative policies on the other differ with respect to their reactions on a macroeconomic external shock. Finally, some reasons for many economists' reservations towards dynamic game theory are identified, and suggestions for a strategy towards a fruitful collaboration between mathematicians and economists in this field are given.