A Formal Analysis of Some Issues in Balance of Power Theories

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Abstract
Two general issues raised in discussions of balance of power theories are considered in this paper: the relationship between, on the one hand, the power ratio goals of nations and the size of the international system and, on the other hand, the system's “war propensity.” These relationships are explored through the application of differential game theory. A mathematical model is proposed in which nations are assumed to operate according to certain dynamics, and to have specified goals and certain information about the international system. The “war propensity” of the system is then defined in terms of dangerous power configurations, and the impact of power ratio goals and system size is considered. Several variations on the basic model are analyzed: (1) systems with or without coalitions, (2) different conceptualizations of the dangerous power distribution, and (3) systems containing different types of nations, to wit, major powers and minor powers.

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