Mind Your Decisions

Focal Points (or Schelling Points): How We Naturally Organize in Games of Coordination

Every Tuesday is a Game Theory article at Mind Your Decisions.

Bike safety is a big topic. Wear a helmet. Follow traffic laws, like halting at stop signs. Don’t go too fast, and make sure your brakes work.

This is all useful advice. It has been beat over my head since elementary school. Nonetheless, it didn’t help me from getting into bike accidents during college. To tackle that problem, I took advice that depended on game theory and the concept of focal points.

Focal Points

Imagine you and a partner are in an experiment. Each of you will be shown a diagram of four boxes and asked to pick one. You will not be allowed to communicate with your partner.

If you manage to pick the same box as your partner, then you both get $10. If not, then both of you go home empty-handed.

Suppose you are playing the game. What box would you pick?

It turns out that the strategy is tremendously simple: for each box your partner picks, you will simply match the pick. The hard part is figuring out what your partner will guess since you cannot communicate with each other.

As you can see, this game has a sense of “team spirit.” Both players would like to pick corresponding strategies for mutual gain. We play these types of games often—an example that comes to mind is how friends coordinate outfits, so no two people end up wearing the same thing. Appropriately, such games go by the name of coordination games.

There is no box that’s “better” than another one. The payoff is simply dependent on picking the same one. If you and your partner are good friends, you might have common knowledge about each other to help you win. You might pick box four, for example, because you know it is your friend’s favorite number.

But what if you and your partner were complete strangers? How might you arrive at the same box?

As the problem is stated, there is no particular box that is better to pick. Both of you would go about picking numbers randomly and just accept the 25% random chance of winning (4 winning pairs out of a possible 16).

But now let’s say the experiment was slightly changed. Imagine instead of being faced with four identical boxes, you and your partner were shown a diagram like this:

Now, which box would you choose?

As you can see, box two is specially marked in red. You might realize that it stands out, and suspect that it would also stand out to your partner, the complete stranger. And that’s the trick.

The special marking makes both players pick box two “naturally.” It’s a form of organizing and communicating without actually being able to talk. Remember, there is nothing special about picking box two. The other equilibriums are the players both picking any of the other boxes. What makes box two special is the marking and attraction to it as a choice.

Such an equilibrium earns the fitting name of focal point. It is also known by the name Schelling point, in honor of the game theorist Thomas Schelling, who introduced the concept in his 1960 book The Strategy of Conflict.

It is worth noting that focal points are dependent on social beliefs. In America, I would think most experiment participants would pick box two because it stood out.

But I can imagine this is not necessarily true cross-culturally. It is possible in another culture that it’s considered bad luck to pick the prominent square. Under that system, the natural choice would be never pick box two.

This is helpful knowledge. Eliminating one choice raises the chances of success from 25 percent to just over 33 percent.

The Bike Game

Avoiding bike crashes is type of coordination game. Bikers want to coordinate to avoid occupying the same real estate at the same time.

Let’s start with a simplified version of the game with two bikers moving in opposing directions:

 

To simplify matters, we can say that each biker has a choice of going straight, moving to his left, or moving to his right.

Crashes occur when both bikers go straight, or when they both swerve to the same path–either left or right.

The remaining combinations, say one goes straight and other swerves right, will result in a safe exchange. There are six “safe” cases compared to the three “crash” cases.

Thanks to the nature of the game, by random chance, it’s twice as likely that the bikers will avoid each other than crash.

Furthermore, there is a focal point that can reduce crashes. We Americans drive on the right hand side of the road, so it is natural that both bikers would swerve to their respective right side.

This rule of thumb helps avoid crashes. Plus, it doubles as a good tip for walking in hallways of American offices.

Unfortunately, our friendly human nature tends to undermine the safe focal point. What many of us do is get nervous and try to make eye contact with the other biker.

When you make eye contact, you feel the need to mirror what the other person is doing. Because you have limited time to respond, you don’t react fast enough. You even ruin the random chance of a safe passage and make crash the likely course.

And that’ why the best advice I ever got about bike safety was this rule: avoid eye contact with an oncoming biker. It’s not mind-blowing advice, nor does it always seem nice, but it is very practical. When you don’t stare at the other person, you both will rely on the focal point of swerving to the right.

(My friends and I joked that the “no stare” advice is virtually impossible to follow when the oncoming biker is attractive. But then the game is different, as you probably wouldn’t mind bumping into that person and starting up a conversation).

Some Students Make the Game More Difficult

As I mentioned earlier, focal points are dependent on culture. While avoiding eye contact gets to the “swerve right” equilibrium for Americans, it fails for many international students who drive on the left side of the road, and have the instinct to “swerve left.”

Then, there is another twist. Some students aren’t playing the game of coordination. They view the interaction more like a game of chicken. These people will never swerve because they don’t want to slow down and often they enjoy the opportunity to yell at others.

The game is also more complicated since there are more variables. The realistic situation involves four-war intersections with high traffic. Now each biker has to coordinate with more than one other biker, and there are more bikers on the road. Even if natural bike safety reduced the crash rate to one percent, an intersection with 1,000 such games played per day would have about 10 crashes. In my opinion, that is just not good enough.

What can be done?

Well think back to the box problem. An experimenter who wanted to see success could nudge participants in the right direction by highlighting a box and essentially manufacturing a focal point. The conclusion is the bike game can be improved with better design.

To get fewer crashes, the design can be changed to create a focal point.

Here’s one implementation: create a bike circle with one way traffic, and have arrows to indicate the direction:

If enough bikers follow the rules, then traffic will flow in one-way. Enforcement should come about naturally. New bikers will also follow the traffic as that will be the safest route.

The bike circle creates its own inefficiency, say, if one’s goal is to simply turn left. But it overall should reduce risk and crashes, which are far more costly.

It’s an interesting enough idea that Stanford is trying it out.

I bet one reason they are trying a bicycle roundabout is because new bikers can figure out the one-way flow of traffic very quickly. This is crucial on a campus with thousands of new students coming in every year.

The lesson: if you are running an event, and want to coordinate many people, consider the design and the idea of focal points to help the operation run smoothly.