Consider the Commuter's game introduced in the videos. Suppose that the existing highway-system is expanded so as to accommodate increased traffic flow. Assume that the journey by highway takes 15 minutes if there is no traffic, and that each additional traveller now causes an additional delay of only .004 minutes for all drivers. Thus, the payoff function for a person who takes the highway is P(n) = 45 .004n. The payoff from taking the train remains S(n) = 15.

(a) Find all Nash equilibria. How many people travel on the train? How many people drive? How long does the commute take?

(b) Compare this equilibrium to the original equilibrium in the Commuter game described in the videos. Does the expanded highway-system reduce commuting time for anyone? Why or why not?