Two firms are choosing output by playing the following game. Demand is linear, P = 20-Q, and marginal cost is 8. Suppose that firm 1 moves first and chooses either monopoly output (M), qm, or Cournot output (C), qe. Firm 2 observes the choice made by firm 1 and chooses one of two output levels: either Stackelberg (follower) output (S), 4s, or Cournot output (C), qe. In this game, each firm has the following strategies: Firm 1 has 2 strategies:S = {M, C'} Firm 2 has 4 strategies: S SS SC CS CC Choose when see M S S C C Choose when see C S S (1) Draw the tree of this game (i.e. represent the game in an extensive form) and write down its payoff matrix. (2) Find all the Nash equilibria of this game. (3) The Nash equilibria do not always make sense in a dynamic game. Determine which of the equilibria in part (2) is sensible. Explain.