The present paper studies the causes and duration of wars by building a war of attrition game, and explores the effect of overconfidence in such settings. During the fight, each player infers his opponent's inclination in surrendering given two psychological biases jointly capturing overconfidence: illusory superiority (overestimation), and over-self-confidence (overprecision). We demonstrate that overconfidence is neither necessary, nor suffcient to have war. Yet, overconfident decision-makers are nevertheless more likely to initiate war, and to remain active longer in a conflict. Moreover, we show that the effect of overestimation on war duration may be non-monotonic, with the duration of wars increasing in overconfidence for lowly overconfident players, and decreasing for highly overconfident ones. We argue that this simple model helps understanding a host of real-world conflictive situations.