Models have been used as analytic approaches to the study of arms races in order to describe and to predict the course and consequence of an arms race. Such models can be either descriptive or normative. The original Richardson model is an example of a descriptive model, one with neither an explicit objective nor an assumption of maximizing behavior. Another example of a descriptive model of an arms race is the stock adjustment model. The normative model, with an explicit goal and the assumption of maximizing behavior, represents another type of model that is intended to explain the underlying motivation for an arms race in terms of goal-directed behavior. One such normative model is the Brito model; another is the differential game model. These four models, two descriptive and two normative, can all be interpreted as variants or extensions of the original Richardson model. The Richardson model, therefore, can be given various interpretations that arise from different approaches to the arms race. Another type of model, which also has a Richardson model interpretation, integrates strategic considerations into the treatment of an arms race and thereby provides a synthesis of the various models, with implications for arms races and the outbreak of war. Yet another approach to arms races is that using heuristic decision rules; here, defense planners use certain rules of
thumb regarding weapons procurement that are based on optimizing behavior, on strategic considerations, or on institutional aspects of the defense bureaucracy.