Army 1, of country 1, must decide whether to attack army 2, of country 2, which is occupying an island between the two countries. In the event of an attack, army 2 may fight, or retreat over a bridge to its mainland. Each army gets 1 from occupying the island and 0 from not occupying it.If they fight, they get 1 from the cost of war, and the island is destroyed.1. (5 pts) Write as an extensive form game.2. (15 pts) Solve this game by backwards induction.3. (15 pts) Suppose that before the potential invasion, country 2 may choose to burn their route of escape. How does this change the solution of the game?4. (10 pts) What does this tell us about commitment at war? Can it ever be better to reduce your options? Why?