Let's suppose that the Intervener faction has the following preference ordering: (Launch coup; Launch coup) > (Stay out; Stay out) > (Stay out; Launch coup) > (Launch coup; Stay out) Let's suppose that the Professional faction has the following preference ordering: (Stay out; Stay out) > (Launch coup; Launch coup) > (Launch coup; Stay out) > (Stay out; Launch coup) The basic game tree for the Military Intervention Game is shown below. Using the preference orderings shown above, write in the appropriate payoffs for each possible outcome. Use the numbers 4, 3, 2, and 1 to indicate the preference ordering for the players. Solve the game using backward induction. a) What is the expected outcome? b) What is the payoff? c) What is the subgame perfect equilibrium