The Olympics, traffic in Central London and a bar in Santa Fe

We all know now about the empty roads and deserted shops, all quite contrary to the official announcements before the Games began. No doubt Transport for London used their massively complicated, expensive models of the transport network 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 has happened. Santa Fe is teeming with high powered researchers, who proliferate in the state of New Mexico.

Of a Thursday evening, many of them enjoyed gathering in the El Farol bar. The problem was, there were lots of them, 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.

Brian Arthur is a highly original British economist who has been based for many years in America. He realised that the decision of whether to go to the bar or not could be set out as a problem in game theory.

Easy to describe: you need to have a strategy which maximises your chances of being there when El Farol is like Baby Bear’s porridge, not too full, not too empty, but just right.

It turns out that it is incredibly difficult to work out what such a strategy might 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. (Minority Games Book)

But these endeavours have not been useless. We do know some things about the game. One thing we know 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 TfL publicity and Mayoral announcements was to get lots of players – the shoppers, workers and tourists who go into Central London – playing the same strategy. In other words, they believed it would be heaving, and decided not to go in.

This was certainly reinforced by social network effects. Decisions were not taken in isolation, but after discussions with work colleagues, friends and neighbours. This made it even more likely that people would arrive at the same decision.

The lesson for policy makers is that in a networked world, less can be more. A bit of smart theory can weigh far more than tons and tons of the massive models beloved of bureaucrats the world over.

Paul Ormerod is an economist at Volterra Partners and the author of Positive Linking: How Network Can Revolutionise the World, Faber and Faber