ABSTRACT
This chapter uses simple mathematical models to explore the relationship between security regimes and arms race dynamics. The main focus is a regime known as collective security, which is receiving wide attention. Little of the attention is mathematical; however, none of it involves dynamical systems. The chapter aims to formalize collective security in a dynamical systems context, which will allow us to extract some unexpected results. The simplest two-country form of Lewis Frye Richardson's classic purely competitive arms race model is presented. In addition to Richardsonian competition and collective security, it examines a regime characterized by the presence of a world policeman, or "globocop." In the usual sensitivity analysis, one uses a fixed mathematical model and examines the sensitivity of that model's outputs to variations in model inputs. An elegant way to proceed would be to characterize mathematically the entire class of formal arms race models under which collective security would show a depressive effect.
