A remark on the arms race spiral

The purpose of this paper is to explain the tendency of escalation of a regular bilateral arms race, or the arms race spiral.

Inspired by the Richardson‐type models, a system of two differential equations is used for describing a bilateral arms race. But the variation of one adversary's armaments and/or military expenditures is not associated with the amount of the other's armaments and/or military expenditures as it is usually done in this type of model. It is linked instead with their variation, as it practically happens in governments' decision‐making processes.

The association of the two variations suggests that when one adversary tends to match the increase of the other's armaments and/or military expenditures, these tend to increase to infinity for a given fixed point in time.

The mathematical result indicates that the tendency of completely matching the increase of adversary's armaments or military expenditures acts as an accelerator that causes the continuous escalation of the arms race. Therefore, as long as a substantial change in the relationship between the two adversaries – implying a complete change of the model's coefficients – does not happen, the arms race escalates, and the so‐called spiral is observed.