Asymmetric burden-sharing and the restraining and deterrence effects of alliances

Alliances are often presumed to serve the dual purpose of restraint and deterrence, though few existing studies examine their relationship and the connection with defense burden-sharing. This research employs a three-player game-theoretic model, which endogenizes the process of alliance formation and arms buildups, to demonstrate how intra-alliance burden-sharing allows the alliance to preserve the status quo. The results suggest that alliance burden-sharing may exert the deterrence and restraining effects, while at most one effect is observable at a time because the effects occur in separate parameter spaces. If a prospective ally's cost of arms buildups is relatively low, a status-quo-oriented superpower may form an alliance even by shouldering a disproportionately heavy burden to dissuade the ally from overturning the status quo (the restraining effect). Conversely, if the cost is relatively high, the superpower may form an alliance to protect the ally from external threats (the deterrence effect). However, to prevent being exploited by this ally, the superpower provides only the units of armed forces that are sufficient to incentivize the ally to bolster its military capabilities to deter the threats. Their alliance entails power aggrandizement, but it does not provoke a non-signatory as the ally remains too weak to act unilaterally.