Problem 1 Four people must drive from A to B at the same time. Each of them must choose a route. Two routes are available, one via X and one via Y (refer to the gure attached}. The roads from A to X, and from Y to B are both short and narrow; in each case, one care takes [1' minutes, and each additional car increases the travel time per car by 3 minutes. (If two cars drive from A to X, for example, each car takes 9 minutes.) The roads from A to Y, and from X to B are long and wide; on A to Y one car takes EU minutes, and each additional car increases the travel time per car by 1 minute; on X to B one car takes 20 minutes, and each additional car increase the travel time per car by .9 minutes. What is the Nash Equilibrium of this game? (Think if all four of the people take the same route, can any one of them do better by taking the other route? What if three people take on route and 1 the other? What if two take each route?) Now suppose that a relatively short, wide road is built from X to Y giving each person four travel options to choose from: AXB, AYB, AXYB, and AYXB. Assume that a person who takes AXYB travels the AX portion at the same time as someone who takes AXB and the YB portion at the same time as someone who takes AYB. (Think of their being a constant ow of trac). On the road between X and Y, one car takes 7 minutes and each additional car increases the travel time per car by 1 minute. Find the Nash equilibrium in the new situation. Compare each person's travel time with her travel time before the road from X to Y was built