Congestion and Game Theory
Source: https://www.heraldmailmedia.com/news/local/highway-congestion-is-maryland-s-approach-wrong/article_b5ea9371-b2a5-5be4-94a0-d9bb39d5f4f0.html
Motorists traveling on state freeways in 2015 experienced a total delay of 47.9 hours and burned 22.6 million gallons of additional fuel due to congestion. Crowded conditions along Interstate 81 in Washington County have also captured public concern due to an increasing number of crashes—some of them deadly. The state recently responded by announcing a $105 million project to begin widening the interstate to six lanes.
However, Matthew Turner and Giles Duraton who study how the U.S. handled highway congestion said through the previous experience this would not work. After a highway is widened, traffic gradually increases until each lane carries about the same amount of traffic that lanes on the load carried before it was widened, a process that takes about 10 years, according to Turner.
And this makes sense in accordance to the game theory. Nash equilibrium is achieved when players are choosing a strategy that is best responses to each other. In this situation, a simpler way to interpret is the opportunity costs for all the people traveling from point A to point B are the same in the case of Nash equilibrium.
Assuming getting from point A to point B, the drivers can either choose “Interstate 81” or “other highway” and Nash equilibrium is reached. Also, assuming that the opportunity cost for people to travel by “car” and “other transportation” are the same. There is also a Nash equilibrium established between different kinds of transportation. It would take the driver exactly the same amount of time to travel either on “Interstate 81” or “other highway”. After the highway is widened, the time would be less if the driver is choosing “Interstate 81”. Thus, people who used to be traveling on “other highway” would shift to “Interstate 81” due to lower opportunity cost represented by a shorter time needed. Due to the decrease in time and waste on petrol, people who used to choose “other transportation” would shift to “car”. These trends would keep on until the Nash equilibrium meets again, which should not differ a lot from the original Nash equilibrium.
In the article, other alternatives like open express toll lanes to provide relief on congested potions, using “smart signals”, and “ramp metering”, which can work better in comparison to just widen the road.