Revisiting the Arms Race Richardson's Model

Abstract

Richardson's model is classical in the field of International Relations, which describes arms race between two actors, by means of system of ordinary differential equations with constant coefficients of the respective military budgets. In this paper, we extend Richardson's model to comprise an arbitrary number of actors to investigate whether there are sca le properties that arise when multiple actors are considered, firstly by treating the special case when the actors are undifferentiated, then the case of differentiated actors. We report that, as the number of actors increases, there is no guarantee that individual budgets will not tend to increase limitlessly, which is a theoretical result not present in the original model and presents new possibilitie s of thinking about the boundaries of international system stability.