1. There are two airline carriers, United and American Airlines, that are deciding how many flights to run from Detroit (DTW) to Seattle (SEA) every day. To simplify the analysis, both firms can choose to run 0, 1, 2 or 3 flights per day. The payoffs for both firms is given in the table below. American 0 United 1 2 3 1 (0,600) 0 (0,0) (450, 450) (600, 0) (700,0) (600, 300) (800,0) (550, 100) 2 (0, 700) (300, 600) (350, 350) (450, 150) 3 (0,800) (100, 550) (150, 450) (300, 300) a. If there was no collusion in this market, how many flights would each firm run every day? (5 pts) b. Suppose that the two carriers colluded and agreed to each run two flights per day. In addition, assume that United values next periods profit at only 90% of this period's profit and American values next period's profit at 80% of this period's profit. Solve for the value of collusion VC and the value of deviation VD for both firms. Is this collusive agreement self enforcing? (5 pts) c. Suppose that the two carriers colluded and agreed to each run two flights per day. In addition, assume that United values next periods profit at only 70% of this period's profit and American values next period's profit at 60% of this period's profit. Solve for the value of collusion VC and the value of deviation VD for both firms. Is this collusive agreement self enforcing? (5 pts) d. Suppose that the two carriers colluded and agreed to each run one flight per day. In addition, assume that United values next periods profit at only 70% of this period's profit and American values next period's profit at 60% of this period's profit. Solve for the value of collusion VC and the value of deviation VD for both firms. Is this collusive agreement self enforcing? (5 pts)