Game Theory Episode 30
The Traffic Game: Phantom Traffic Jams; Google Maps Conundrum; Paradoxical Solutions
One of the most dangerous things a person can do during the course of a day is to get into a personal vehicle and take to the streets.
According to the National Highway Traffic Safety Agency, roughly 38,680 people died in motor vehicle accidents in the U.S. in 2020, up more than 2,500 hundred from the previous year.
More than 283 million motor vehicles in operation in the United States can make for some seriously clogged roadways and stressful trips.
Traffic, of course, is a system involving players, risks, and payoffs. That means our old friend game theory might be able to help us negotiate the roadways safely and efficiently. But unfortunately, the incentive-driven nature of game-theoretic systems can actually work against us.
As frustrating as it can be, we don't always have design-forward solutions to complex systematic problems. In fact, sometimes trying to design solutions can actually make things worse for everybody.
Game theory tells us that rational actors in a system are generally incentivized to make self-interested decisions.
Think back to the Nash Equilibrium: every player in a given system assumes every other player knows what each player's optimum strategy is, and no player has any reason to change his or her own personal strategy.
Applied to traffic, the "game" is to figure out how to get to one's destination in the shortest, safest way possible.
There are only so many routes to get from A to B, and although the number of drivers in any system is finite, anyone who has to commute on busy urban streets or crowded highways knows it feels like the traffic can be endless.
The decision-making process is thus about which routes to take to minimize the amount of time spent sitting in the car (listening to your favorite podcast to pass the time).
Traffic is tricky, though. With so many variations in game conditions -- like different start and endpoints for different drivers, multiple available routes, varying speeds with which drivers choose to drive (ranging, of course, from the curious octogenarian rubberneckers to those on the road looking to try out for the Indy 500) -- it seems sensible that human beings ought to be able to design a system of traffic that benefits virtually everyone in some kind of overall-optimized system.
Yet, combined with the historical foibles of established towns and roadways that make some systems permanently sub-optimal, the multitude of system variables actually makes it so hard to design a system that adding additional routes and shortcuts in the network can actually make traffic worse, not better.
That phenomenon is called Braess's Paradox. Named for German mathematician Dietrick Braess, the paradox states that shortcuts in roadway networks offer rational, self-interested drivers a "more optimal" route to their destination than the original road network, which redistributes traffic into a denser flow and results in longer individual drive times.
One consequence of the paradox is that over-engineering road networks to include additional outlets, or even simply increasing the volume through which dense traffic can flow, could make problems worse for the overall system -- and make things slower for drivers than they would have been in the first place.
Consider the elevator, for example.
You need to climb a flight of stairs to the 10th floor of a building. If 100 people a day arrive at similar times, they all have to take the laborious walk up to the 10th floor. The trip is tedious, but it only takes as long as it takes for each person to make the walk.
If one day the building installs an elevator, almost every self-interested person looking to make a shorter, easier trip to the 10th floor via the lift would be incentivized to take it.
But elevators have limits: if only 5 people can take a ride at a time, that means twenty trips to the top for all 100 people.
Such an arrangement might be fine if they all trickle in slowly, but if they keep their normal schedule and arrive close to one another, some people may be better off taking the sub-optimal walk up the stairs than waiting for as many as 20 trips required to take everyone where they want to go.
One possible conclusion for drivers might be that it is sometimes better to take the "less-than-perfect" route to get from one place to another.
We live in a world of live updates on GPS, so in theory, we can select better routes if conditions change once we are actually on the road.
However, in practice, even with live updates, the GPS network may not be able to account for the number of drivers that opt to take suggested shortcuts or alternate routes. Dense traffic that gets re-routed to a longer route -- specifically to avoid a slowdown -- is still dense traffic.
The only difference is that the density on the original route might decrease for a time.
The next time you have to take a trip, especially if that trip is unusual or goes through heavily trafficked areas, consider that every little shortcut or new route suggestion might actually end up costing you more time in the long run.
Instead, plan ahead, and read road conditions as well as you are able without blindly following the advice of a cell phone.
Game theory is just math, and even though your handheld computer is better at math than you are, that doesn't mean you should assume it has your best driving interests at heart.
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