Alliances in Anarchic International Systems

Abstract

Alliances play a central role in international relations theory. However, aside from applications of traditional cooperative game theory that ignore the issue of enforcement in anarchic systems, or interpretations of the repeated Prisoners' Dilemma in the attempt to understand the source of cooperation in such systems, we have little theory on which to base predictions about alliance formation. This essay, then, builds on an n-country, non-cooperative, game-theoretic model of conflict in anarchic systems in order to furnish a theoretical basis for such predictions. Defining an alliance as a collection of countries that jointly abide by "collective security strategies" with respect to each other but not with respect to members outside of the alliance, we establish the necessary and sufficient conditions for an alliance system to be stable. In addition, we show that not all winning or minimal winning coalitions can form alliances, that alliances among smaller states can be stable, that bipolar alliance structures do not exhaust the set of stable structures, and that only specific countries can play the role of balancer.