Complete Solution to Richardson's Arms Race Equations

Abstract

Richardson's arms race equations, dx/dt=ky - ax + g, and dy/dt=Ix - by + h, and their more complex variants have been mainly used empirically for data fitting the simplifications a = b and k = I. Furthermore, only the additive form, d(x+y)/dt=(k-a) (x+y)+(g+h), is usually tested while the complementary expression in (x-y) is ignored. This paper gives the complete solution of the above equations, in an easily testable form. Richardson's 1907–1914 data are found to agree with the arms race model but they also could be explained by a simpler self-stimulation model.