1.1 Textbook Page 243, Chapter 8, 8.4 Exercise, Question 1 There are 1000 cars which must travel from town A to town B. There are two possible routes that each car can take: the upper route through town C or the lower route through town D. Let a: be the number of cars traveling on the edge AC and let 3; be the number of cars traveling on the edge DB. The directed graph in the gure below indicates that travel time per car on edge AC is a: / 100 if as cars use edge AC, and similarly the travel time per car on edge DB is y/ 100 if y cars use edge DB. The travel time per car on each of edges CB and AD is 12 regardless of the number of cars on these edges. Each driver wants to select a route to minimize his travel time. The drivers make simultaneous choices. (a) Find Nash equilibrium values of (r and y. (b) Now the government builds a new (one-way) road from town C to town D. The new road adds the path ACDB to the network. This new road from C to D has a travel time of 0 per car regardless of the number of cars that use it. Find a Nash equilibrium for the game played on the new network. What are the equilibrium values of as and 3/? What happens to total costoftravel (the sum of total travel times for the 1000 cars) as a result of the availability of the new road? (0) Suppose now that conditions on edges CB and AD are improved so that the travel time on each edge are reduced to 5. The road from C to D that was constructed in part (b) is still available