Here is a game theory puzzle for you. The government proposes to build a highway between the two cities, A and B, that reduces the burden of the existing freeway. Here is the rationale behind the proposal.
There are two modes of arriving from A to B: 1) take the train, which takes 20 minutes, or 2) take the freeway using a car, which takes (10 + n/5) minutes, where n is the total number of cars on the road. Since the train is a public transit, it doesn’t matter how many people take it – it always takes 20 minutes to reach the destination. But if the new highway operates, the travel time becomes (5 + n/5) minutes. Note that the old freeway stops functioning once the new road is available.
What is your view on building the highway as a solution to reduce travel time, or are there alternate ideas to meet the objective?
The existing case
Suppose there are 100 commuters. Each can take the train and reach B in 20 minutes. That gives a few people the advantage of taking cars and reaching their destination earlier – until the travel time matches the following way.
20 = 10 + n/5
n = 50
Beyond 50 commuters, car travel will take longer than the train; therefore, 50 is an equilibrium number in the longer term.
The new case
The new equilibrium is estimated as follows:
20 = 5 + n/5
n = 75
In other words, more people will take the new route, but the travel time remains the same.
The paradox
This is a simplified game-theory explanation of what is known as the Downs–Thomson paradox. It says that comparable public transport journeys or the next best alternative defines the equilibrium speed of car traffic on the road.
Alternatives
On the other hand, if modifications are possible to reduce the commute time of the train, then overall travel time (for both railways and roads) can be reduced.
References
Downs–Thomson paradox: Wiki
The Problem with Faster Highways: William Spaniel
