Braess’s Paradox in Seoul, South Korea
Braess’s Paradox in Seoul, South Korea
https://www.forbes.com/sites/quora/2016/10/20/bad-traffic-blame-braess-paradox/#29a8f9d514b5
Adding roads in the traffic network can sometimes decrease the speed at Nash equilibrium. This phenomenon is called Braess’s Paradox.
For example, assume 4000 drivers want to go from S to E.
At the initial state without road AB, there are 2 strategies (paths): SAE and SBE. If both paths are used, then Nash equilibrium happens when both paths have the same travel time
x/100+ 45 = 45 +y/100 , x + y = 4000
Nash equilibrium occur when x = y = 2000
Travel time = 2000/100 + 45 = 65
Travel time will be 65 minutes for all drivers
To reduce the travel time, road AB with travel time 0 was added. There are 3 strategies: SABE, SAE and SBE
Travel time for SABE = x/100+ 0 +y/100
Travel time for SAE = x/100+ 45
Travel time for SABE = 45 +y/100
Compare SA and SB.
If x = 4000, travel time for SA = 4000/100 = 40
Travel time for SB = 45
Travel time for SA is always less than SB, so every traveler uses SA, x = 100
Compare AB and AE.
Travel time for AB is 0 which is less than travel time for AE 45.
Everyone will use AB, then use BE to arrive at E
Nash equilibrium occurs when x = y =100.
SABE is a dominant strategy.
If all travelers use SABE, travel time = 4000/100+ 4000/100 = 80 minutes
After adding the road with travel time 0, the travel time increased by 20 minutes.
Drivers are selfish. They choose paths that would be fastest for themselves. Therefore, all drivers want to use the shortcut. Individual drivers choose SA road because it has the shortest travel time. However, they increase the travel time for other drivers on the road and decrease traffic speed. Adding the shortcut increases travel time at Nash Equilibrium. A real-life example of Braess’s Paradox is Cheonggyecheon Restoration Project in Seoul, South Korea. A six-lane highway was removed to create waterways and recreation parks. Government officials expected that the change would make traffic congestion worse and decrease traffic speed in the area. However, the traffic speed increased after the highways were removed while the amount of traffic remained the same. The highways represent the road with short travel time (AB) in the example. Removing the highways decreased the travel time at Nash equilibrium. The example illustrates Braess’s Paradox that the addition of roads with shorter travel time sometimes increases travel time at Nash equilibrium.