Coordination in the El Farol Bar problem: The role of social preferences and social networks

The El Farol Bar problem, introduced by [1], has over the years become the prototypical model of a system in which agents, competing for scarce resources, inductively adapt their belief-models to the aggregate environment that they jointly create. The works on the El Farol Bar problem which retained the best-reply learning of that seminal model show that, if the agents make use of global information, the aggregate attendance keeps fluctuating around the threshold level. Works where best-reply behavior has been replaced with reinforcement learning show that the system converges to an equilibrium characterized by a group of agents who always go to the bar and a group of agents who always stay at home. In this paper, we first introduce social networks: in our model, the agents take their decisions on the basis of their neighbors' past decisions. We investigate the effect of two network structures: the circular neighborhood and the von Neumann neighborhood. Simulations show, first, that the system always reaches a state of perfect coordination and, secondly, that many kinds of equilibria emerge, each of which is characterized by a certain number of classes in terms of attendance frequency. We then modify this network-based model by introducing minimum attendance thresholds. Simulations show that even with very low minimum attendance thresholds the equilibrium characterized by perfect equality is the most likely outcome. In particular, we show that it takes just one fourth of the agents with 'Keep-up-with-the Joneses' behavior to always lead the system to the perfect equality equilibrium.

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