Braess’s Paradox, Induced Demand, and Market Clearing Prices of Travel
Braess’s Paradox argues that the addition of an edge in a network, especially a traffic network, has the possibility to create a Nash Equilibrium that decreases the benefit of every single player in the network. But will the new arrangement after a change actually be a point of equilibrium?
Although Nash Equilibrium is widely defined as a stable state when roads are added or removed an addition or reduction in traffic is often seen overall as well. There have been multiple instances when the deletion of a road has improved traffic conditions, but it has also completely reduced the number of people driving altogether. A French newspaper commented on the apparent “evaporation” of vehicles. A bridge had been removed because of damage, and other routes experienced an increase in volume. The counts for the total number of cars, however, seemed to decrease from the expected traffic volumes seen before the bridge closure. The deletion of the bridge had removed some of the drivers altogether. This change can be attributed to what some may refer to as induced demand, which is a very basic economic phenomenon. As supply increases, the quantity that the market consumes will increase. Conversely, a decrease in supply will drive a decrease in quantity consumed by the market. Here we can think of the number of roads as the supply and each driver as a consumer of part of the road.
This brings to question where the legitimate stable state lies (and if there is one at all). If a road is deleted or added, urban planners must now factor in the decrease or increase that this will cause to the total number of travelers. Additionally, urban planners must attempt to realize where these individuals are “materializing” from or “evaporating” to. Many individuals who use these roads every day may very well be commuting, or traveling because they have to. These can be thought of as individuals who are required to travel to their destination and will do so by any means reasonable. The article cited above, however, noted that a separate occasion of a roadway being removed saw a 49.5% drop in total vehicles. Could it be true that 49.5% of travelers could simply decide that traveling to their destination was not an option? I would argue not. These travelers would then be required to find a different mode of transportation be it carpooling, which deletes a vehicle from the network but not a traveler, or public transportation. This switch from a vehicle to a different form of transportation could be seen as a switch from one good to another in a matching problem, as the price of the goods is adjusted to clear the market. The deletion of roads could be equated to a rise in the price of a product that sees too much demand from a constricted set.
We can then think of the addition of a road as a possible decrease in the price of traveling in a personal vehicle because more people find they maximize their value and will travel on the road. Similarly, a decrease in the number of roads could be an increase in the price of traveling in a personal vehicle, as more individuals seek to find more valuable options or are priced out of the market altogether (although we’d like to think a substantial amount of people still would need to travel regardless of how many roads lead to their destination). This increase and decrease in the price of traveling would correctly match the movement of the supply curve in a basic supply and demand graph which would predict higher prices and lower quantity bought as supply decreases and lower prices and higher quantity as the supply increase. It is important to think of the “price” in this situation as a tool that could be employed rather than just a cost. The high price can drive travelers to choose an alternative: an event that may be favorable to the city and environment. It could be argued then that a solution to the multitude of problems created by a vast amount of personal vehicles would be the strategic deletion or closure of roads. Not only would travel times have the potentiality to increase if the number of travelers remained equal, but some of the travelers would decide not to travel on the road at all. As the market clears and consumers react to changing circumstances, the removal of excess roads could be helpful.