Binghamton University, State University of New York.
Artif Life. 2021 Nov 2;27(2):113-130. doi: 10.1162/artl_a_00347.
The El Farol Bar problem highlights the issue of bounded rationality through a coordination problem where agents must decide individually whether or not to attend a bar without prior communication. Each agent is provided a set of attendance predictors (or decision-making strategies) and uses the previous bar attendances to guess bar attendance for a given week to determine if the bar is worth attending. We previously showed how the distribution of used strategies among the population settles into an attractor by using a spatial phase space. However, this approach was limited as it required N - 1 dimensions to fully visualize the phase space of the problem, where N is the number of strategies available. Here we propose a new approach to phase space visualization and analysis by converting the strategy dynamics into a state transition network centered on strategy distributions. The resulting weighted, directed network gives a clearer representation of the strategy dynamics once we define an attractor of the strategy phase space as a sink-strongly connected component. This enables us to study the resulting network to draw conclusions about the performance of the different strategies. We find that this approach not only is applicable to the El Farol Bar problem, but also addresses the dimensionality issue and is theoretically applicable to a wide variety of discretized complex systems.
埃尔法罗酒吧问题通过一个协调问题突出了有限理性的问题，在这个问题中，参与者必须在没有事先沟通的情况下单独决定是否参加酒吧。每个参与者都提供了一组出席预测器（或决策策略），并使用前一周的酒吧出席人数来猜测给定周的酒吧出席人数，以确定酒吧是否值得参加。我们之前展示了如何通过使用空间相空间，使人口中使用的策略分布稳定到一个吸引子。然而，这种方法是有限的，因为它需要 N-1 个维度来完全可视化问题的相空间，其中 N 是可用策略的数量。在这里，我们提出了一种新的相空间可视化和分析方法，通过将策略动态转换为以策略分布为中心的状态转移网络。一旦我们将策略相空间的吸引子定义为一个汇点-强连通分量，所得到的加权有向网络就可以更清楚地表示策略动态。这使我们能够研究所得到的网络，从而得出关于不同策略性能的结论。我们发现，这种方法不仅适用于埃尔法罗酒吧问题，而且还解决了维度问题，并且在理论上适用于各种离散化的复杂系统。
