Скачать или смотреть The Hidden Benefits of Toll Roads: A Game Theory Puzzle

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There are two ways to reach downtown. The first is the trolley. It is capable of handling a ton of commuters, so it takes 20 minutes regardless of how many ride it. The second is a highway. It is subject to congestion, so the travel time is 5 + x/4, where x is the number of drivers.

There are two types of commuters. 40 impatient individuals lose 2t in utility from their commute, where t is the time to the destination. The remaining 60 individuals are patient and only lose t instead.

The puzzle: is there a toll you could impose on the highway that no one would object to? You will have to calculate a couple of different Nash equilibria and their associated payoffs to find the answer.