Excerpt

Nobody goes there anymore. It’s too crowded.—Yogi Berra

With some papers, it is clear that they will become an instant classic. W. Brian Arthur’s 1994 “Inductive Reasoning and Bounded Rationality (The El Farol Problem)” is such a paper. Like many classics, it starts with a question anyone can understand: Suppose going to a bar is only pleasant if not too many people show up. How do you decide whether to go? This “bar problem” was inspired by the popular El Farol bar in Santa Fe.1 But, of course, this toy problem is an exemplar of a much more general class of problems: How do people divide a scarce resource  among  themselves?  Yet  game  theory—the  discipline that studies interactive decision-making—is ill equipped to address it. Classical game theory posits that players will coordinate on one of the equilibria of the game. The argument, roughly speaking, is this: If the system is not in equilibrium, then at least one of the players could gain by changing their action. For example, if few people are going to the bar one night, then at least one player would be better off if they attended rather than staying home. And even if people face this problem repeatedly (say, every Thursday night), it is far from clear the system would converge to an equilibrium. Of course, people can look at past attendance to predict how many people will go. But if everyone uses the same forecasting model, then predictions are bound to be invalidated: If all believe few will go, all will go; and if all believe most will go, nobody will go. So, if some stationary state is to emerge, it will involve persistent heterogeneity.

Bibliography

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Kets, W. 2011. “Learning with Fixed Rules: The Minority Game.” Journal of Economic Surveys 26:865–878. https://doi.org/10.1111/j.1467-6419.2011.00686.x.

Kets, W., W. Kager, and A. Sandroni. 2022. “The Value of a Coordination Game.” Journal of Economic Theory 201:105419. https://doi.org/10.1016/j.jet.2022.105419.

Miller, J. H., and S. E. Page. 2009. Complex Adaptive Systems. Princeton, NJ: Princeton University Press. Neumann, Von, and Morgenstern. 1944. Theory of Games and Economic Behavior. Princeton, NJ: Princeton University Press.

Sandholm, W. H. 2010. Population Games and Evolutionary Dynamics. Cambridge, MA: MIT Press. Zermelo, Ernst. 1913. “Über eine Anwendung der Mengenlehre auf die Theorie des Schachspiels.” In Proceedings of the Fifth Congress of Mathematicians, 501–504. Cambridge University Press. Cambridge.

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