Army A has a single plane with which it can strike one of the three possible targets. Army B has one anti-aircraft gun that can be assigned to one of the targets. The value of target k is Vk with vi > V2 > 03 > 0. Army A can destroy a target if and only if the target is undefended and A attacks it. Army A wishes to maximize the expected value of the damage and army B wishes to minimize. Note that this is a zero sum game. 1. Formulate the situation as a normal form or matrix game. 2. Suppose vi = 5, 02 = 4, V3 = 3. Find an equilibrium in which Army A attacks all three targets with positive probability. For extra credit argue that all equilibria have this property. 3. Suppose v1 = 3,02 = 2,03 = 1. Find an equilibrium in which Army A attacks only the first two targets with positive probability. For extra credit show that this game has a unique equilibrium