Colonel Blotto has 2 divisions with which to defend 2 mountain passes. His opponent also has 2 divisions. Blotto successfully defends a pass if and only if he allocates an equal or greater number of divisions to it as his opponent. Blotto wins if he successfully defends both passes, and loses otherwise. Blotto's payoff is 1 if he wins, 0 if he loses; the opponent's payoff is 1 if he wins, and 0 if he loses.

(i) Find a mixed-strategy Nash Equilibrium of the game.

(ii) Is there any other Nash Equilibrium of this game? If so, find the other Nash Equilibrium(a). If not, show that the first equilibrium you found is the unique equilibrium. To reach your answer, use the algorithm for finding all the Nash Equilibria of a game.