. Two airline carriers, United and Delta Airlines, are deciding how much to charge for their daily flight from Detroit (DTW) to Seattle (SEA). To simplify the analysis, both firms can charge either a low price (L), a medium price (M) or a high price (H). The payoffs for both firms is given in the table below. Delta L M H L (5, 5) (12, 4) (14, 2) United M (4, 12) (10, 10) (18, 9) H (2, 14) (9, 18) (13, 13) a. Suppose that both firms have to choose their price simultaneously. What price will each firm charge. What is each firm's payoff? b. Now suppose that United has to choose its price before Delta. Draw the extensive form (game tree) of this game. What is the subgame perfect equilibria of this game? How does it compare to your answer in (a)? c. Suppose that again both firms are choosing prices simultaneously but instead of playing the game once, the game is played infinitely between United and Delta. Is it possible for the two firms to collude in order to both charge a medium price? What is the minimum discount factor required in order to sustain such an agreement? d. Is it possible for the two firms to collude in order to both charge a high price? What is the minimum discount factor required in order to sustain such an agreement?