A comparative analysis of different expectation models for the El Farol Bar problem

Abstract

The El Farol Bar Problem is first discussed by W. B. Arthur (1994) and he presents this problem to introduce a new field that he names as “complexity economics”. The El Farol Bar Problem is widely used in the literature, especially in congestion and coordination studies. In this study, we model the El Farol Bar Problem using the agent-based modelling methodology and Python computer language. We create different agent types with distinctive expectation models. The emergent behaviors of different agent types are compared with respect to several performance measures. After several experiments with different agent types, we reach two important conclusions: The heterogeneity of the decisions is the key factor in obtaining low standard deviation of attendance values and the assumption of knowing the bar capacity value is crucial for a good performance. Agents who make expectations randomly generate the highest heterogeneity in the attendance values, which is consistent with the findings in the literature. In this thesis, we also introduce agents who use exponential smoothing method in forming expectations. They create low heterogeneity in decisions and a poor performance compared to other agents. Nevertheless, the exponential smoothing method works well in learning the capacity value. Accordingly, we introduce an agent type that combines random attendance expectations with the exponential smoothing method in estimating the capacity. When the bar capacity is unknown, this agent type produces mean attendance values gravitating towards the bar capacity ensuring the heterogeneity in the decisions. Lastly, we develop Yasarcan-Çetiner agents that do not use expectation models, but a hysteresis structure in decision-making. Although, they do not have explicitly coded capacity learning mechanism in their algorithms, they still learn the bar capacity as a swarm according to their emergent collective behavior.