IT NOW seems like a distant memory, as London has again filled up with shoppers, tourists and people celebrating Team GB’s historic gold medal haul. But last week, the city was notoriously labelled a ghost town, despite official predictions that the capital would be heaving. No doubt, Transport for London had used its hugely complicated and expensive transport network model to deduce that the system would be under massive strain.
But a deceptively simple game, devised in the 1990s about a bar in Santa Fe, sheds light on what actually happened.
Santa Fe is a US city teeming with high-powered researchers, who proliferate widely in the state of New Mexico. Of a Thursday evening, many of them enjoyed gathering in the El Farol bar. The problem was that there were lots of researchers and the bar was rather small. If it got too crowded, each scientist would have preferred to stay at home. But, if it was too empty, it was no fun to go for a drink after work.
Brian Arthur is a highly original British economist who has been based in the US for many years. He realised that the decision of whether to go to the bar or not could be set out as a problem in game theory. You need to form a strategy which maximises your chances of being at El Farol when it is not too full, not too empty, but just right.
It turns out that it is incredibly difficult to work out what the best strategy should be. Swiss scientists Damien Challet and Yi-Cheng Zhang developed the problem into the so-called “minority game”. Literally thousands of high-powered maths papers have been written on this. But no strictly rational way of playing the game has been devised.
These endeavours have not been useless. We do know some things about the game. One of the most important is that, if everyone determines the same strategy, regardless of what it is, it is guaranteed to fail. If you think the bar will be empty, you will go – but so will everyone else. And vice versa, if you think it will be full.
The effect of all the Transport for London publicity, and mayoral announcements on the Tube, was to get lots of players – the shoppers, workers and tourists who go into central London – pursuing the same strategy. In other words, they believed the city would be heaving, and decided not to go in.
This was certainly reinforced by social network effects. Decisions were not taken in isolation, but followed discussions with work colleagues, friends and neighbours. This made it even more likely that people would arrive at the same decision.
The lesson for policymakers is that, in a networked world, less can be more. Massive bureaucratic modelling, or elaborately planned public campaigns, are not the only solutions to strategic dilemmas. In fact, they can be counter-productive. A little smart theory can prove much more effective.
Paul Ormerod is an economist at Volterra Partners and the author of Positive Linking: How Networks Can Revolutionise the World (Faber and Faber).