Shedding light on El Farol

We mathematize El Farol bar problem and transform it into a workable model. In general, the average convergence to optimality at the collective level is trivial and does not even require any intelligence on the side of agents. Secondly, specializing to a particular ensemble of continuous strategies yields 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.