(20 points) Three countries (A, B, and C) must decide whether to declare war on a common enemy. A country cannot win the war alone, but if two or three countries declare war together, they will win for sure. Each country's payoff is described by the following rule: Let n be the total number of countries that declare war on the enemy. If a country declares war (D), its payoff is equal to 10ifn=1 40 ifn=2 60 ifn=3 If a country does not declare war (N), its payoff is equal to 0. (a) Find all purestrategy Nash equilibria if the three countries decide simultaneously. Write down the game matrix and show your work. (8 points) For parts (b) and (c), assume that the three countries decide sequentially: rst A, then B, then C. Each country knows what the previous country(/ies) had decided. (b) Write down the game tree and find the subgame perfect equilibrium. Clearly write down each country's strategy in the equilibrium. (7 points) (c) Find a Nash equilibrium that is not subgame perfect. Explain why it is a Nash equilibrium. (5 points)