I saw this tweet and it immediately reminded me of Brian Arthur’s El Farol equilibrium story.

For those who don’t know it, El Farol is a bar in Santa Fe, where Arthur is based. It has great Irish music but the problem is that it’s no fun if the bar gets too crowded. What is the outcome in this situation where people are trying to choose based on beliefs about what others will choose? There is no ‘deductively rational’ solution to this choice problem. In his paper, Arthur writes: “If all believe few will go, all will go. But this would invalidate that belief. Similarly, if all believe most will go, nobody will go, invalidating that belief. Expectations will be forced to differ.” Simulating behaviour of 100 agents repeatedly shows that mean attendance at El Farol quickly converges to 60, but with large swings from period to period, and changing identity of those attending – it isn’t always the same 40 with a varying number of extras. “while the population of active predictors splits into this 60/40 average ratio, it keeps changing in membership forever. This is something like a forest whose contours do not change, but whose individual trees do. These results appear throughout the experiments, robust to changes in types of predictors created and in numbers assigned.”

The Waze problem looks similar. If you see congestion on your planned route, you’ll switch to an alternative – perhaps – for you also have to predict how many other people will switch too, and whether the initial congestion will stay or vanish if there are enough other users of similar apps.

Later work on El Farol found one game theoretic solution: individual agents adopt a mixed strategy, whereby each has a fixed probablility of choosing either El Farol or an alternative bar. Another is that after a period of learning, agents sort themselves into groups, those who always go and those who always stay home. But I don’t think these work for Waze-style congestion problems which are not repeated.

Indeed, real-time apps are surely creating more of these kinds of co-ordinated decision problems.

Brian Arthur’s book [amazon_link id=”B00SLUR9HI” target=”_blank” ]Complexity and the Economy [/amazon_link]is a nice introduction to his work.

[amazon_image id=”B00SLUR9HI” link=”true” target=”_blank” size=”medium” ]Complexity and the Economy: Written by W. Brian Arthur, 2014 Edition, Publisher: Oxford University Press, USA [Hardcover][/amazon_image]