In this dissertation, we consider a two-person zero-sum game in which a fighter with a missile wishes to destroy a bomber. The bomber has much small-caliber ammunition for protecting itself from the fighter. And the fighter possesses a missile for attacking the bomber. We develop models for the behavior of the fighter, in terms of missile launch time, and of the bomber, in terms of ammunition firing rate, in several situations. In particular, we examine extensions of the Weiss-Gillman model and the Karlin model