Army A has a single plane with which it can strike one of 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 v$1>$ v$2>$ v$3>0.$ Army A can destroy a target only if the target is undefended and A attacks it$.$ Army B can only get the value of the target if the target is defended and A attacks it$.$ Otherwise, the payoffs are $0.$

$$ Formulate the situation as a normal form game.

$$ Determine whether the game is strictly competitive. $$ Find the Nash equilibrium of the game.