1. (20 points) Two agents 1 and 2 need to travel from point A to point B (see figure). Each of them must choose a route. Two routes are available. One route goes through X and the othyer one goes through Y. The road from A to X and from Y to B are both short and narrow.; in each case one car takes 6 minutes and each additional car increases the travel time per car by 3 additional minutes. The roads from A to Y and from X to B are long and wide; ; on A to Y one car takes 20 minutes, and each additional car increases the travel time per car by 2 additional minutes. On X to B one car takes 20 minutes, and each additional car increases the travel time per car by 2 additional minutes. Each driver gets a gross benefit of 40 \"utils\" by travelling from A to B. Thus the payoff of each driver is the gross benefit minus the total travel time from A to B. The diagram is shown below (Figure-A). The entries in parentheses are the costs per car for each segment. The first entry is when one car uses that segment. The second entry is for 2 cars using the same segment. (6,9) (20,22) (6,5) Figure-A (a) Formulate the above problem as a Normal form game (5 points) (b) Find all the NE in the game (15 points)