Richardson Arms Race Model

The Richardson arms race model, set out by Lewis Fry Richardson in Arms and Insecurity (1960), is a pair of coupled differential equations describing how two rival states adjust their armaments over time. Each state's rate of arming rises with the rival's level of arms (action–reaction fear), falls with the burden of its own existing arms (fatigue or economic constraint), and is shifted by underlying grievance or goodwill. Analyzing the system reveals whether an arms race converges to a stable equilibrium or spirals upward without bound, making it the foundational mathematical model of arms competition.