Highways get bigger, traffic doesn’t get better
Despite ever increasing highway width, it is hard to break what is known as the “iron law of congestion”. This Bloomberg article delves into some reasons why this is the case, namely, political motivations and incentive structures. Generally, whenever a resource decreases in cost, it will be used in more new ways, in this case the resource being road space. This idea of induced demand is largely argued why despite building more lanes of a road, the traffic flow will usually catch up after some time. I also found this related to something called the Marchetti Constant, which is the idea that the amount of time people spend commuting is about an hour total, or thirty minutes each way, regardless of how far people are going– as people get better transportation, they simply commute further distances for similar amounts of time as when they traveled on their own two feet. These two facts seem to go hand in hand: as road space is cheaper, people will keep filling that road until there is a better second alternative (which feels like precisely the Nash equilibria learned in class). On the side of the policy makers, there is also game theory at play. One would think that it would be the job of the policy makers to try to decrease the amount of total travel time for everyone possible. However, in practice, policy makes often do things that won’t necessarily help the public if it supports their own cause. For example, in the article, gas taxes are cited as a way to help decrease traffic, but also directly lower the budget of the Department of Transportation, who are the very people who make such policy, therefore, making gas taxes too high isn’t in favor of the DOT. Given incentives like this, and because the introduction of new roads will temporarily increase the throughput of the road, policy makers can usually point to adding new roads historically as working in the short term as justification for building more roads. This turns into a perpetual cycle of traffic being bad, adding new lanes to lower traffic, which induces more traffic making traffic bad, leading to a loop in the cycle of building yet more lanes. Is it policy makers fault that traffic is bad, or will people always just commute for the same amount of time, regardless of how cheap things get? It is a hugely complicated problem, but I think that incentive structures for policy makers is a huge point of failure.
There is an interesting perspective on both networks and game theory at hand for not only commuters, but the people who make the means of public transport (whether it be more roads, trains, or something else). Although the game theory we have learned in class always considered cars that had to get from one point to another, we never considered the potential payoff of doing such a commute. Consider for example if we assigned payoffs for each traveler for their commute from arbitrary nodes A and B. Although this could be complicated in practice, we could think of this as the joy someone may get from their new location, or the economic opportunity of a job at the new location. If the payoff is not high enough, some travelers would simply choose to not go at all. From an initial reaction, this seems to be a more realistic model, since in practice many people will not wait an infinite amount of time in traffic, and choose not to make commutes if they have a better alternative. Solving this type of problem by hand for only a few travelers can get quite hairy– image only 10 travelers traveling across 5 nodes. There is a potential payoff of each node and the cost of getting to said node depends on the strategies of the other players. We saw finding Nash equilibria by hand for only three players started to get tedious– imagine this type of game with hundreds of players, hundreds of strategies, and hundreds of payoffs! Additionally, because the models we used in class are relatively simple, it is hard for us to see things like how long it takes for people to switch routes. We assume everyone knows what route everyone else takes but the reality is that after a new road is built, it will take time for people to switch back and forth until reaching new Nash Equilibria. We could introduce another variable of time to our problems, and even model what people do by each day. This type of stochastic model would introduce some more fidelity, so we could model how fast people change strategies, but also much more complexity, and also force us to make more assumptions about peoples behavior.
Perhaps the more important perspective to consider is the game theory perspective of the policy makers. Consider the example above for the Department of Transportation and the gas tax. In class, we learned about Nash equilibria and how people will take the best response to the other players. If we consider our two players to be policy makers and the public, there are two strategies for the policy makers, and only a single strategy for the public. The public has to pay their tax, and a policy maker can either raise or lower the tax. However, what is the payoff for each group? Since there is only a single strategy for the public, there is nothing they can do to affect their payoff, however, for the policy makers, it seems that their payoff is in how much influence and power they can incur, which is best done by maximizing the money they can collect from car drivers. This model of the game between politicians and the public is quite naive: in reality, there are a lot of factors to consider about making new roads for a policy maker. Besides the time it would take for commuters to make their travels, there are ethical concerns of displacing and negatively affecting communities around the areas that will be turned into roads, as well as environmental concerns, which could directly negatively affect politicians on a long enough time horizon. Designing a game that accurately captures the incentives of policy makers is extremely difficult, and adding new factors to consider does not scale linearly with respect to the complexity of the game. Looking at the decisions policy makers make around traffic, it is clear the Nash equilibria we are in does not also guarantee mutual benefit for the public.
I would recommend to read the full article (first link below), because it does a really good job relating some of the concepts in class to things that happen in practice, and places them well in the greater context of politics, ethics, and society.
Sources: Bloomberg Article, Lewis-Mogridge Position Wikipedia, Marchetti Constant Wikipedia, CS 2850 Course Textbook.