Show that the travel time is worse

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Reference no: EM131445825

Question: This is an exercise on Braess's paradox. Consider the traffic system in which travelers want to go from A → C. The travel time for each car depends on the total traffic.

(a) Suppose the total number of cars is 6 and each car can decide to take A → B → C or A → D → C. Show that 3 cars taking each path is a Nash equilibrium.

(b) Suppose a new road B → D is built which has travel time zero no matter how many cars are on it. Cars can now take the paths A → B → D → C and A → D → B → C in addition to the paths from the first part. Find the Nash equilibrium and show that the travel time is now worse for all the players.

Reference no: EM131445825

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