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Learning in the Santa Fe Bar Problem

This paper investigates learning in the Santa Fe (El Farol) bar problem (sfbp). It is argued that rationality together with belief-based learning (e.g., Bayesian updating) yields unstable behavior in this game. More specifically, two conditions normally sufficient for convergence to Nash equilibrium, namely rationality and predictivity, are shown to be incompatible. Low-rationality learning algorithms, however, converge to the symmetric Nash equilibrium in sfbp. Although it is fair, this equilibrium is suboptimal—the expected utility of the collective is near zero. This paper therefore proposes a simple modification to sfbp, whereby agents that attend the bar are charged an entry fee that is divided equally among those agents who do not attend the bar. In this modified scenario, low-rationality algorithms, which once again learn Nash equilibrium strategies, approximate Pareto-optimal behavior: individual rationality coincides with collective rationality.