Equilibrium Concepts for Arms Race Problems.

In this paper we have presented various possible behaviors of two nations in an armaments race. The conceptual aspects and the properties of the Cournot and Stackelberg solutions in terms of the information about the armaments behavior of the other nation have been discussed. The static solution is simplest since it requires a myopic behavior on the part of each nation; i.e. each nation adjusts its armaments level according to the current armament level of the other nation and with no consideration to any future goals. The dynamic solutions on the other hand where future goals are incorporated in the decision making at any instant of time requires more assumptions about the behavior of the other nation. Two cases have been discussed in conjunction with the Cournot solution. In the first, each nation predicts the future armament variations of the other nation, while in the second, each nation predicts the future armaments expenditure policy of the other nation as a function of the armaments levels of both nations. From a practical point of view, such solutions would be useful in a situation where a noncooperative equilibrium is to be negotiated (e.g. Middle East conflict) and each nation is asked (or forced) to commit itself to a certain armaments level or expenditure policy over a certain period of time in the future. The nations are in dynamic Cournot equilibrium if the predictions match the optimum quantities. The dynamic Stackelberg solution on the other hand has been discussed for a situation where armaments decisions are obtained as a function of armaments levels at stages in time by a leader nation first and then by the follower nation.
Proceedings of NSF Conference on Control Theory in International Relations Research, Indiana Univ., Bloomington, Ind. Apr 75.