Shedding light on El Farol
We mathematize El Farol bar problem and transform it into a workable model. We find general conditions under which the convergence of the average attendance to the resource level is trivial and does not even require any intelligence on the side of agents. Secondly, specializing to a particular ensemble of continuous strategies leads this problem to a model similar to the Minority Game. Statistical physics of disordered systems allows us to derive a complete understanding of the complex behavior of this model, on the basis of its phase diagram.