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	Richardson Arms Race Model	Power Transition Analysis
Field	International Relations	International Relations
Family	MCDM	Process / pipeline
Year of origin	1960	1980
Originator	Lewis Fry Richardson	A. F. K. Organski & Jacek Kugler
Type	Coupled linear differential-equation dynamic model	Theory-driven observational analysis of war between rising and dominant powers
Seminal source	Richardson, L. F. (1960). Arms and Insecurity: A Mathematical Study of the Causes and Origins of War (N. Rashevsky & E. Trucco, Eds.). Pittsburgh: Boxwood Press; Chicago: Quadrangle Books.	Organski, A. F. K., & Kugler, J. (1980). The War Ledger. University of Chicago Press.
Aliases	Richardson Arms Race Equations, Arms Race Dynamics Model, Action-Reaction Arms Model, Richardson Model of Arms Competition	Power Transition Theory Analysis, Power Parity and War Analysis, Hegemonic Transition Analysis, Overtaking and War Analysis
Related	3	3
Summary	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.	Power transition analysis examines when and why war breaks out between a dominant state and a rising challenger as their relative power converges. Originating in A. F. K. Organski and Jacek Kugler's The War Ledger (1980), it holds that the international system is hierarchical and most dangerous not at moments of clear preponderance but when a dissatisfied rising power approaches parity with the dominant state — and it operationalizes this by tracking relative national capabilities over time and relating overtaking to the onset of major war.