Focal points and minibuses

It’s 1975. You’re on vacation in New York City, and you’ve made plans to meet an old friend, also on vacation there, tomorrow. The problem is that you don’t have their phone number or any other way to get in touch with them, and you didn’t agree on a place or time to meet. Where do you go to meet your friend – and at what time?

The above is one of my favorite game theory problems, because it is one that even non-experts can solve. It is interesting in that there are many “correct” answers – any place in the city, and any time, will work, as long as both you and your friend make the same choice. But what time and place will maximize the chances of that happening? I’ve thrown out the problem in a number of casual conversations, and the modal answer is 12:00 noon in front of the clock at Grand Central. Since the essence of the game is to guess what the other person will do, this is also the right answer in that it maximizes the chance that you and your friend will win – the “focal point” of the game. It’s also the answer that Tom Schelling got when he tried this problem out back when he invented it.

I was reminded of this problem by a recent post on what is easily my favorite new development blog, NPR’s Goats and Soda, that covered the reversal of the Kenyan government’s ban on decorating minibuses. A bit of background: minibuses, which go by various names in different countries, are the chief means of public transit in most of eastern and southern Africa. They work along fixed routes, and often for fixed fares (in Malawi it is technically illegal to raise prices unless a government board approves a fare hike). A minibus will typically sit at the origin point for its route until it is totally full, and then head to the end point.

Commuters are thus faced with a problem: there are lots of minibuses at the bus stop. I want to take the one that leaves soonest since it will arrive sooner. Which one do I board? NPR says it is the one with the most garish decorations, because “if young people prefer a painted bus that plays loud music, and they seem to, then it fills up faster”. That is the right answer – but the wrong reason! I would bet money that the painted bus will fill up faster even if there are no young people around or they don’t prefer it, because it is an obvious focal point for the game.

Minibus operators are very aware of this focal point problem, and employ multiple techniques to solve it. One approach is collective action: some bus stops have an enforced queue of buses*, so customers can only board the first one in the line. Another one that I particularly like involves faux customers called “timing boys” who board the bus and sit on it until it is nearly full, then get off (usually to a hail of jeers from the actual commuters). Since a fuller bus is more attractive (and anyway an obvious focal point even if customers are aware of the ruse), this attracts customers quicker and leads to faster departures. Policymakers should keep in mind that when a minibus owner gets “CNN BREAKING NEWS” spraypainted onto his bus, it’s more than just for fashion – it makes the transit network more efficient.

*In Malawi these queues are often enforced by cabals of stationary bandits known as “touts”, who impose an effective tax on the bus operators.