Prospect theory is an empirical model of choice that stands as the leading alternative to rationality for explaining decisions under conditions of risk. While many still defend the assumption of rationality as an appropriate starting point for the construction of international relations theory - deterrence theory especially - there is growing support for models of international politics grounded in the actual capacities of real-world decisionmakers. This article accepts that standard depictions of deterrence incentives capture much of the essential character of deterrent relationships. However, it substitutes cognitive assumptions in place of traditional rational choice. Using prospect theory, the article reconsiders three typical deterrence games. The new model of military deterrence put forth unearths a set of conditions that are required for successful deterrence and uncovers a set of causes for deterrence failures that run counter to conventional understanding.