There are two cities, A and B, joined by two routes, I and II. All roads are one-way roads. There are 100 travelers who begin in city A and must travel to city B. Route I links city A to city B through city C. This route begins with a road linking city A to city C which has a cost-of-travel for each traveler equal to 0.5 + x/200, where x is the number of travelers on this road. Route I ends with a highway from city C to city B which has a cost-of-travel for each traveler of 1 regardless of the number of travelers who use it. Route II links city A to city B through city D. This route begins with a highway linking city A to city D which has a cost-of-travel for each traveler of 1 regardless of the number of travelers who use it. Route II ends with a road linking city D to city B which has a cost-of-travel for each traveler equal to 0.5 + y/200, where y is the number of travelers on this road. These costs of travel are the value that travelers put on the time lost due to travel plus the cost of gasoline for the trip. Currently there are no tolls on these roads. So the government collects no revenue from travel on them.

(a) Draw the network described above and label the edges with the cost-of-travel needed to move along the edge. The network should be a directed graph as all roads are one-way.

(b) Travelers simultaneously chose which route to use. Find Nash equilibrium values of x and y.

(c) Now the government builds a new (one-way) road from city C to city D. The new road is very short and has 0 cost-of-travel. Find a Nash equilibrium for the game played on the new network.