Using a simple bargaining game, we investigate how strategic interactions are shaped by preferences, technology, and endowments. We study whether changes in relative military capabilities make conflicts more likely and find a nonmonotonic relationship between the cost of conflict and the probability of conflict. The game has strategic complements if the cost of conflict is small and there is a large first-mover advantage and has strategic substitutes otherwise. This characterization generates predictions regarding the use of strategic investments—for example, in defense systems. An extension of the model shows how expanding one’s territory today may increase the risk of conflict tomorrow.

A big power is facing a small power that may have developed weapons of mass destruction. The small power can create strategic ambiguity by refusing arms inspections. We study the impact of strategic ambiguity on arms proliferation and welfare. Strategic ambiguity is a substitute for actually acquiring weapons: ambiguity reduces the incentive for the small power to invest in weapons, which reduces the threat of arms proliferation. But strategic ambiguity hides information, and this can lead to costly mistakes. Cheap‐talk messages can be used to trigger inspections when such mistakes are particularly costly. Tough messages that trigger inspections always imply a greater risk of arms proliferation.