Game theory and traffic
by Chetan Parikh
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In a wonderful book, well worth reading, “Traffic”, the author, Tom Vanderbilt, writes on game theory and traffic.


“Your daily drive may not seem to have much to do with the strategies of the Cold War, but every time two cars approach an unmarked intersection simultaneously, or four cars sidle up to a four-way stop at about the same time, a form of game theory is being applied. Game theory, as defined by the Nobel Prize-winning economist Thomas Schelling, is the process of strategic decision making that occurs when, as in a nuclear standoff or a stop-sign showdown, "two or more individuals have choices to make, preferences regarding the outcomes, and some knowledge of the choices available to each other and of each other's preferences. The outcome depends on the choices that both of them make, or all of them if there are more than two.”


Traffic is filled with these daily moments of impromptu decision making and brinksmanship. As Schelling has argued, one of the most effective, albeit risky, strategies in game theory involves the use of an "asymmetry in communication." One driver, like Barrios Gomez in Mexico City, makes himself "unavailable" to receive messages, and thus cannot be swayed from going first through the intersection. These sorts of tactics can be quite effective, if you feel like risking your neck to prove a bit of Cold War strategy. Pedestrians, for example, are told that making eye contact is essential to crossing the street at a marked crosswalk (the kind without traffic lights), but at least one study has shown that drivers were more likely to let pedestrians cross when they did not look at the oncoming car.


Drivers at intersections are acting from a complicated set of motives and assumptions that mayor may not have anything to do with traffic law. In one study, researchers showed subjects a series of photographs of an intersection toward which two vehicles, equally distant from the intersection, were traveling. One had the legal right-of-way, and the other did not; the second driver also did not know if the first driver would take the right-of-way. Subjects were asked to imagine that they were one of the drivers and to predict who would "win" the right-of-way under a variety of conditions; whether they were making eye contact, whether they were a man or a woman, and whether they were driving a truck, a medium-sized car, or a small car. Eye contact mattered hugely. When it was made, most subjects thought the driver who had the legal right-of-way would claim it. Drivers were also more likely to yield when the approaching car was the same size. They were even more likely to yield when the driver was female-an artifact, the researchers suggested, of a belief that women drivers were less "experienced," "competent," or "rational." Or was it just chivalry?


Traffic is thus a living laboratory of human interaction, a place thriving with subtle displays of implied power. When a light turns green at an intersection, for example, and the car ahead of another driver has not moved, there is some chance that a horn will be sounded. But when that horn will be sounded, for how long and how many times it will be sounded, who will be sounding the horn, and who the horn will be sounded at are not entirely random variables.


These honks follow observed patterns that mayor may not fit your preexisting notions. We've already seen that drivers in convertibles with their tops down, less cloaked in anonymity, were less likely to honk than other drivers. For a similar reason, drivers in New York City, surrounded by millions of strangers, are likely to honk more, and sooner, than a driver in a small town in Idaho, where a car that has not moved might not be a random nuisance but the stalled vehicle of a friend. What the driver ahead is doing also matters. One study showed that when a car was purposely held as the light changed to green, drivers were more likely to honk-more often and for a longer time-if the nonmoving driver was quite obviously having a cell phone conversation than if they were not. (Men, it turned out, were more likely to honk than women, though women were just as likely to visibly express anger.)


All kinds of other factors-everything from gender to class to driving experience-also come into play. In another classic American study, replicated in Australia, the status of the car that did not move was the key determinant. When the "blocking car" was "high-status," the following drivers were less likely to honk than when a cheaper, older car was doing the blocking. A study in Munich reversed the equation, keeping the car doing the blocking the same (a Volkswagen Jetta) and looking instead at who did the honking; if you guessed Mercedes drivers were faster to the horn than Trabant drivers, you guessed right. A similar study tried in Switzerland did not find this effect, which suggests that cultural differences, like the Swiss reserve and love of quiet, may have been at work. Another study found that when the driver of the blocking car was a woman, more drivers - including women - would honk than when it was a man. An experiment in Japan found that when the blocking drivers drove cars with mandatory "novice driver" stickers, the cars behind were more likely to honk than when they did not (perhaps the horn was just a driving "lesson"). A study across several European countries found that drivers were more likely to honk, and honk sooner, when the stalled driver ahead had an identity sticker indicating that they were from another country than when they were fellow nationals.


Men honk more than women (and men and women honk more at women), people in cities honk more than people in small towns, people are more reluctant to honk at drivers in "nice" cars-perhaps you already suspected these things. The point is that as we are moving around in traffic, we are all guided by a set of strategies and beliefs, many of which we may not even recognize as we act upon them. This is one of the themes guiding a fascinating series of experiments by Ian Walker, a psychologist at the University of Bath in England. In a complex system such as traffic, Walker says, where myriad people with a loose sense of the proper traffic code are constantly interacting, people construct "mental models" to help guide them. "They just develop their own idea of how it works," Walker told me over lunch in the village of Salisbury. "And everyone's got different ideas."”