The Reliability of Alliances and Extended Deterrence: A Game-Theoretical Analysis

Abstract

This article develops a stochastic dynamic model to explain the breakdown probability and the deterrence effect of alliances by taking into consideration both expected long-run streams and short-run shocks. With this model, the traditional results are restated and reconfirmed by formal theorems. It proves that alliance members break their commitments very often, because of their inability to set a complete conditional alliance to rule out every costly short-run shock. This formal model also shows that an alliance has a deterrence effect when the ally of a target-member is strong enough to defeat a potential attacker if it starts an attack, and the alliance is never used. When the potential attacker is uncertain whether the rescuer-partner is actually strong or weak, the model is then extended to the deterrence game with incomplete information, through which the rescuer-partner signals to the potential attacker that it is strong, thereby increasing the potential attacker’s posterior probability about the rescuer being strong. We then find that, under the pooling strategy and the separating strategy, the reliability of alliances is enhanced and successful deterrence becomes more likely. Finally, the Taipei-Beijing-Washington triangular relationship is analyzed as an example of our formal theory.