An Analysis of the Richardson Arms Race Model

According to Lewis Richardson, the likelihood of two nations engaging in conflict can be determined by a set of differential equations. Richardson conjectured that a nation’s probability of entering into an aggressive war is based upon its stockpiles of available weaponry, and tempered by the resistance of the citizenry. In the Richardson model, the likelihood of a small dispute erupting into a full war is based upon these variables, and the current conditions. The model has three basic cases: both nations tending towards disarmament, both nations tending towards a runaway arms race, and both nations tending towards a stable equilibrium point. Lewis Fry Richardson (1881-1953) was a British mathematician and physicist who made several advances in the fields of geophysics, scaling, and fractality. His 1922 book, ”Weather Pioneering by Numerical Processes,” was the first to suggest techniques of numerical integration which could be applied to atmospheric motion. Richardson worked at the United Kingdom Meteorological Office until 1920, when it was incorporated into the Air Ministry. He then left to teach at a British university until his retirement in 1940. Richardson, a man devoted to the ideals of peace, attempted to come up with mathematical expressions for war. He toiled with this work from 1940 until his death, and the results were published posthumously in 1963. One of the conclusions of his research was a system of differential equations modelling arms races. This system has become known as the Richardson Arms Race Model, and has been subject to analysis and refinement since being published. The basic system is: