The El Farol Bar Problem as an Iterated N-Person Game

The famous El Farol Bar problem [1] is an excellent demonstration of the self-referential expectation formation. As such, it serves also as a simple model of financial markets. A number of agents must decide independently each week whether to go to their favorite bar or not. If an agent expects that the bar will be overcrowded, he will stay at home; otherwise, he will go to the bar. If all agents believe few will go, then all will go, destroying all the expectations. On the other hand, if all agents believe many will go, then nobody will go, destroying the expectations again. Arthur [1] has shown by using computer simulation based on a sophisticated reasoning that the bar attendance fluctuates rather wildly around the capacity level of the bar. This result was arrived at by many other researchers as well (e.g., [2–4]). The El Farol problem has been extended to the so-called minority game [5]. The players must choose between two options and those on the minority side win. Many variants of this game have been developed, a large number of papers have been published (e.g., [6–9]), and even books have been written about it [10–12]. In this paper, a much simpler approach is proposed.