Last week I wrote about the Slow-up event and the question of reducing car traffic. I also mentioned that reducing traffic is a question of incentives.
In Switzerland, the citizens will be voting on June 5th over a motion to direct the currently collected taxes on fuel in full to the upkeep of the road network. As in many EU countries, the different taxes, including a mineral oil tax or an excise duty and the value-added-tax, the total price of fuel in Switzerland contains over 50% taxes.
The motion argues that by directing the collected fuel taxes to the upkeep of the road network clear benefits will be gained:
- streets will become safer in the living areas as heavy traffic is rerouted to new routes avoiding these areas
- traffic jams can be reduced by building more capacity. This will also reduce the costs of lost time spent in traffic jams.
Both listed benefits focus on the aspect of added capacity, since adding capacity supposedly directs traffic outside of living areas and also reduces traffic congestion.
Added capacity does not necessarily reduce traffic jams but adds throughput
At first the adding of capacity seems like an intuitive answer to rerouting traffic and reducing traffic jams, but a game theoretic analysis shows this is not necessarily the case.
With an existing capacity C of the traffic network an individual person has the choice of using his own car, taking public transport or postponing (or even cancelling) his trip. As long as the time TC by own car is the same or lower as the time TB used by taking public transport, the individual will take his own car. Also, when the traffic starts jamming (or the person expects traffic jams), he will postpone or even cancel his trip, if the value T of the time lost in the traffic jam is higher than the gained benefit B of making the trip. As the traffic consists of multiple individuals making these evaluations, the amount A of traffic on the streets is limited by inequalities TC < TB and T < B. As long as these two inequalities hold, more people will be taking their own car and will be making their trips, instead of postponing or cancelling them. On balance people are indifferent between their options, each according to their individual valuations.
I am assuming here that most people have roughly the similar values of TC, TB, T and B: since most people are “ordinary” (in the central portion of the bell-curve) in many aspects, it is reasonable to assume that they value their time quite similarly. This means that while an individual person might choose co postpone his trip. because the traffic network is already full, he might do the same try another day, thus “forcing” another person with the same values of T and B to abstain from traveling that day. It is worth mentioning that some individuals with extremely high values of B might never end up postponing their trip.
Now, let’s observe what will happen, when the capacity of the road network is increased to C2 > C. It immediately follows that the travel time, whether by own car or by public transport is lowered, since there is more space for the current amount of traffic A. Also, taking own car becomes more profitable and the inequality TC < TB will hold , since the public transport is always slowed down by its fixed routes and required stops. Since the use of own car becomes more profitable and the value of making the trip exceeds the value of postponing or cancelling it, more trips will be made by own car and the total amount of trips made will increase. This increase will continue, until the inequalities TC < TC and T < B no longer hold, at which point people as a whole are again indifferent between their respective choices.
Now we have a larger amount of traffic A2 > A (i.e. vehicles on the road) than before and people are using the same amount of time for their travel, since the increase in traffic takes place at the margin (T < B and TC < TB) where we have a lot of people with similar preferences. When, for some people, TB > TC and T < B, they take public transport, so the increased capacity contributes to the use of own car and the total amount of people traveling. The increase in road capacity did not reduce the congestion or travel times, but just increased the use of own car and the number of trips made.
Changing the payoffs changes traffic
We observed that with added capacity of the road network, people will increase the use of own car and will complete their trips as long as TC < TB and T < B. This observation directly points out, that changing behavior requires changing people’s payoffs. It is also necessary to be careful about, whose payoffs should be changed, to have the desired effect. To observe a change in a person’s equilibrium strategy-mix, the payoff’s of others must to have changed, so that the first person is again indifferent between his choices in the new equilibrium. If, as the mentioned motion suggests, traffic is to be reduced, each individual person would be traveling less on average in equilibrium. It then follows that the benefits of traveling in relation to its costs would have to be lower than initially.
A strategy-mix can be interpreted as:
- the probability of a single person choosing a specific pure strategy
- a person’s expectations towards the other players’ choosing a specific pure strategy
- a portion of players playing a specific pure strategy.
In the case of traffic jams, the first and third interpretation are the most obvious ones. We would a observe a person traveling less, when all other people were indifferent between traveling or postponing their travel after their payoff for traveling would have been reduced. Likewise, we would observe people, to whom travel is less valuable, traveling less, if at all, while people, to whom travel is more valuable, would still be traveling.
Increase costs, decrease traffic
To reduce traffic jams, the cost of trips made has to be higher in comparison to the value gained from making the trips, if the amount of traffic is to be reduced. For example, by imposing road tolls such that their costs exceed the value gained from taveling, some people will choose not to travel or postpone their travel to a time, when the collected road tolls are lower or the value of the trip is higher. Here it has to be observed that collecting road tolls on some roads only redirects traffic to roads without tolls. This movement continues, until the value of the time lost in traffic jams on the roads without tolls equals the cost of the road tolls, at which point people are indifferent between using a toll road or one without tolls. To decrease traffic overall, its costs relative to the value gained have to increase on all possible routes.
From the motion’s viewpoint this means that in order to reduce traffic and therefore increase the traffic safety in living areas, heavy traffic would have to be more costly in those areas. Another option would be to ban heavy traffic in those areas, but this would lead to potential congestion and too much traffic on other routes. Just adding capacity by building side routes means that more traffic in total can pass through, but in equilibrium the amount of traffic through the living areas will be such, that it takes as long to reach the destination as it would take by taking the route avoiding the living areas.