Shedding light on El Farol

TL;DR

This paper models the El Farol bar problem using statistical physics, revealing that collective optimality emerges trivially without agent intelligence and connecting it to the Minority Game for deeper analysis.

Contribution

It transforms the El Farol problem into a formal model, applying statistical physics to analyze its complex behavior and phase transitions.

Findings

Average convergence to optimality is trivial without agent intelligence

Model similarity to the Minority Game is established

Complete understanding of the model's phase diagram is achieved

Abstract

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.