Differential games results for military expenditures of unequal antagonists in the third world

In developing countries, resources are scarce and military expenditure can hinder development. Thus, allocation of resources between defense and civilian sectors is an important decision. Also, in developing countries, most defense spending is related to regional conflicts where one frequently encounters unequal participants (e.g., India—Pakistan, Iran—Iraq, China—Vietnam). In such situations, the bigger power aspires to be the regional leader, and allocates resources to the defense sector accordingly.

A model incorporating the two above mentioned stylized facts has been examined by Deger and Sen 1] in two different ways. They first look at the problem from a single country's point of view, which takes the other's reaction function as given, and show that in the long run, military expenditures and armament stock levels will exhibit stability. Next, they formulate the problem as a noncooperative differential game in which each country assumes knowledge of the other country's welfare function, and conjecture that stability will once again be exhibited. The present paper attempts to verify that conjecture using a simplifying assumption which is necessary to be able to qualitatively solve the problem. This simplifying assumption does not change the results for the optimal control models, however, the conjecture is not valid for the simplified differential game model.