The El Farol problem goes digital

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

AdamRFisher
Please develop an app that simulates Waze recommendations to assess which routes will open up based on everybody else follow Waze.
13/05/2015 07:12

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 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]

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6 thoughts on “The El Farol problem goes digital

  1. Pingback: The El Farol problem goes digital | Homines Economici

  2. That was an excellent program – it dealt with issues that seem talked a lot about now, so it was quite ahead of its time.

    I have a few points:

    – About the discussion around El Faro, the uncertainty about others’ response etc – Keynes knew about it way back when with the beauty contest analogy:

    “”It is not a case of choosing those [faces] that, to the best of one’s judgment, are really the prettiest, nor even those that average opinion genuinely thinks the prettiest. We have reached the third degree where we devote our intelligences to anticipating what average opinion expects the average opinion to be. And there are some, I believe, who practice the fourth, fifth and higher degrees.”

    He still modelled the economy fairly mechanically with linear functions, though.

    – John Gaddis says “It matters because the social sciences are supposed to
    tell us what is going to happen in society.” But as Jon Elster says in his introduction to the social sciences:

    “Sometimes we can explain without being able to predict, and sometimes predict without being able to explain.”

    – The main point I take away from this is that skepticism must be foremost among the intellectual virtues – and that anyone trying to understand or change the world should be deeply skeptical of what they can know or achieve.

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