A Dynamic Model of an Armaments Race

THE ECONOMIC EFFECTS OF ARMAMENTS RACES is a problem that has been neglected by economists. The work that has been done has, with a few exceptions, been done by non-economists or by economists who work at the interface of economics and political science or operations research. Models that treat the economic aspects of the problem have been static, and models that have considered the dynamics of armaments races have ignored the economic aspects. This essay is an attempt to integrate these two lines of research and derive a dynamic economic model of an armament race. In this paper we will show that if each country attempts to allocate resources optimally between consumption and arms, the resulting dynamic equations are similar to Richardson's equations.2 There are several schools of thought about the stability of armament races. One is that armaments races have a stable equilibrium. This result comes either from a static model that treats an armament race as a game similar to "Prisoner's Dilemma" or from dynamics model such as Richardson [8], Saaty [9] and Smoker [10, 11] have presented. The dynamic models have two problems: first, the equations of motion are assumed; second, they assume myopic behavior on the part of the participants. A second belief is that armaments races are unstable. This theory, often seen in the popular press, holds that unless some agreement is reached weapon stocks will increase in an ever increasing spiral that must ultimately lead to bankruptcy or nuclear holocaust. A third view is that a stable equilibrium may exist, but that the stability may only be a local property. Thus a large disturbance of the system (e.g., the introduction of a new weapons system> may cause an armaments race. This view was most recently expressed in Wiesner et al. [12] during the recent ABM debate. One purpose of thispaper is to formulate a model that will permit us either to reconcile or to discriminate between these apparently conflicting viewpoints. We shall address the problem by considering a system with two nations. Each nation can use its production for either consumption or investment in its weapons