Burning Bridges: An island between countries A and B is in dispute. The island is connected to Country B's mainland by a bridge. The island is currently occupied by B's Army. A's army is deciding to attack the island or not. In the event of an attack, Army B may fight or retreat over the bridge to its mainland, allowing Army A to occupy the island. Both armies prefer to occupy the island rather than not to occupy it, and a fight is the worst outcome for both armies, (a) Find the subgame perfect equilibrium strategies, and the associated outcome of the game, (b) Is it conceivable that Army B could increase its subgame perfect equilibrium payoff by burning the bridge? Explain you answer using an extensive form game.