An evolutionary approach to the El Farol game

A well known problem in economics is to describe properly a situation where N agents are repeatedly competing to use the same limited resource. A version of this problem is known in the literature as the El Farol game: week after week N agents face the decision whether to go or not to go to a bar (named El Farol) which is not big enough for all of them. The game was introduced by Brian Arthur (1994) who used computer simulations to generate the aggregate attendance time series arising from the interaction of the agents. We consider here an evolutionary framework to model the same situation. The advantage of our approach is that the aggregate attendance is given in term of a low dimensional dynamical system and no simulations are needed. Our first outcome is that even a simple setting gives the same results as have been found by Arthur. To give a further insight into the problem a general property of the dynamic "competitive" equilibrium which arises is characterized. Applicability of the model extends also to problems of congestions due to the exploitation of scarce resources (such as encountered in traffic jams, on the internet or in financial markets).