Nash Equilibrium Strategies for the Problem of Armament Race and Control

The problem of modeling and "optimally controlling" an arms race situation between two nations is a very interesting application, of differential game theory. In this pacer, armament, buildup between two nations is modeled as a multistage game problem. The closed-loop Nash, strategy is suggested as a possible solution concept for this problem and it is shown that if the cost functions are quadratic, then the system together with its closed-loop Nash strategies will have the same structure as the well-known Richardson's model of arms race. Consequently, it is suggested that the coefficients in Richardson's model can be determined (or predicted) based on the solution of this multistage discrete game problem. A computational procedure based on the solution of a set of recursive equations is also presented. This type of analysis is not only useful for guiding the armament decision-making process of a nation in an arms race with another nation but also is helpful in assessing economic and military aids by a large nation to smaller nations in an arms race.