Tuesday, April 7, 2009

Economist's Notebook: Game Theory and Stop Signs

The recent attention to the so-called "Idaho Stop" bill that would allow bicyclists to slow but not stop in residential intersections with stop signs got me thinking about this and about the uncontrolled intersections present in many Portland neighborhoods. How should we think about human behavior in the face of such incentives? In these cases, since the problem is inherently about more than one vehicle (or pedestrian) the interactions are strategic in nature, so game theory is the appropriate modeling framework which to employ.

Before we get to that however, Joseph Rose in The Oregonian claims that having an "Idaho Stop" law is actually safer based on incident data from Idaho pre and post law. [Note to Mr. Rose: correlation is not causation, and even if you think this law is good, please explain how such a law could be responsible for an immediate 14.5 percent reduction in bicycle injuries? I think we are dealing with spurious correlation here] But the rationale for the Idaho stop is the same for cars: if there are no other cars around, why stop fully? Sure a bike is human powered but the physical concept is identical, it takes more energy to stop and start than to maintain momentum, and if we care about climate change why not let cars do it too?

Which brings me the the topic of today: non-controlled intersections. These are intersections without any traffic restrictions - anything goes. Well not really, the right of way goes to the vehicle that gets there first, which is precisely the problem. [By the way, do you know who goes if it is a tie? Yep, the vehicle on the right, just like a 4 way stop] Anyway, most of the intersections around my son's elementary school are uncontrolled even though there are many kids walking to school crossing at these intersections. And if you ever want to see good examples of dangerously aggressive driving, all you need to do is show up at an elementary school at drop off times. These are parents who should be most attentive to child safety, but hey their kid isn't walking so they have nothing personal at stake except for getting to work on time. Anyway, I am constantly amazed at the reckless driving exhibited by these parents and what I have found most striking is that on the rare days that I drive my child to school and slow almost to a complete stop at these intersections to be sure there are no cars or kids around, a car from half a block away will almost always bomb right through at 30 mph. If I had asserted my right of way, we would crash and so this reckless driving is kind of like a credible threat in game theory and the logical thing for me to do is to wait until the car has passed.

I imagine that traffic engineers think that these intersections are actually traffic calming. They force all cars to slow down and proceed cautiously through the intersection. But when you think about the game cars are involved in, it is not at all clear that this is the equilibrium. Here is a depiction of a normal form game (single shot, simultaneous, non-cooperative) that I think describes the incentives. Car 1's payoffs are the first number of the pair and Car 2's payoffs are the second number.

Each car has two strategies available to them: be cautious or aggressive when entering the intersection. If both cars are aggressive, a fender-bender occurs and they both loose 10. If they are both cautious, they have to slow down, but no accident occurs so they both get 0. If one is aggressive and the other cautious, the aggressive one gets to go fast and first through the intersection and gets 10 while the cautious gets 0 again. Economics students will immediately recognize the Nash equilibria - where each car is playing a best response strategy to the other. They are the two aggressive/cautious pairs. The problem is of course when both think its the other that is going to be cautious and both end up aggressive... But anyway, this actually describes pretty well what I observe around my son's school: some drivers being aggressive and bombing through the intersections and others being cautious.

This is not what I believe the traffic engineers think and what's worse it means there are aggressive drivers bombing through intersections when lots of little kiddies are running about. Makes me wonder why, of all places, are the intersections around schools not controlled? And, by the way, if you really want to calm traffic, a four-way stop seems to do a good job.


jessibeaucoup said...

You just hit on one of my pet peeves! I go by a school zone every morning. I drive 20 MPH though that school zone not just because it's the law but also because I care about the kiddies. Nearly every morning, a car ZOOMS past me to pull into the school parking lot. So, does that mean that I care more about their kids than I do? Also, are they hoping to raise a generation of irresponsible drivers and lawbreakers? Just curious...

Barbara Powell and Joe Doniach said...

See http://www.theatlantic.com/doc/200807/traffic

Patrick Emerson said...


Interesting, but I am not at all convinced. Glaringly, in his suppositions about why UK drivers get into fewer accidents he doesn't even think to compare driver education. I have a sneaking suspicion UK residents are required to have much more education than the basically none here.

Of all distractions on the road, I don't really think stop signs are that nefarious.

Barbara Powell and Joe Doniach said...

Yes, I'm sure you're right about the level of driver education required by the Brits. I've heard from many people that the driving test is much, much harder than in the U.S.

David S. said...

Some of these problems can be attributed to just plain ignorance of the laws/expectations.

Many people falsely believe that one of the streets in many uncontrolled intersections is the "main street", so they ignore the right-of-way laws/conventions because they don't think they apply. They conveniently ignore that not everyone driving in the area is a local, so they might not know which street is the "main street."

There's a similar ignorance of crosswalks; i.e. virtually all intersections, marked or unmarked. But most drivers don't know this.

I think increased driver education on current laws would lead to a better outcome.

lisamona said...

Maybe we could request some roundabouts from our city planners. They improve the flow of traffic and decrease accidents. Very common in Britain by the way. http://www.iihs.org/research/qanda/roundabouts.html

no one said...

thank you, thank you, thank you! i live in a neighborhood full of uncontrolled intersections and schools and watching the way people drive i was beginning to think i was the only person that saw the absurdity of the whole thing.

Unknown said...

The stronger rationale for allowing bicycles to treat stops signs as yield signs, is that we can stop much faster and have a much wider range of vision, giving us an advantage over car drivers.