The El Farol Bar Problem Revisited: Reinforcement Learning in a Potential Game

We revisit the El Farol bar problem developed by Brian W. Arthur (1994) to investigate how one might best model bounded rationality in economics. We begin by modelling the El Farol bar problem as a market entry game and describing its Nash equilibria. Then, assuming agents are boundedly rational in accordance with a reinforcement learning model, we analyse long-run behaviour in the repeated game. We then state our main result. In a single population of individuals playing the El Farol game, learning theory predicts that the population is eventually subdivided into two distinct groups: those who invariably go to the bar and those who almost never do. In doing so we demonstrate that learning theory predicts sorting in the El Farol bar problem.