Deterrence and arms races: An optimal control systems model

A mathematical model representing the notion of deterrence theory, as depicted in the literature, is studied. This model applies to decision processes of supranational systems. A nation deters its adversary by its capacity to absorb a first attack and to render a retaliatory attack. To construct the model representing this, concepts from the optimal control theory are used. The optimal policy is derived and the parameters in the model are estimated from defense expenditures of various nations involved in three post‐World War II arms races. From the model so constructed, the stability properties of three current arms races are analyzed.