Network-based phase space analysis of the el farol bar problem

Shane St. Luce*, Hiroki Sayama

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)113-130
Number of pages18
JournalArtificial Life
Issue number2
Publication statusPublished - 2021 Nov 2
Externally publishedYes


  • Agent-based modeling and simulations
  • Dynamical systems
  • El Farol Bar problem
  • Game theory
  • Network science
  • Phase space analysis

ASJC Scopus subject areas

  • Computer Science (miscellaneous)
  • Ecology, Evolution, Behavior and Systematics
  • Biochemistry, Genetics and Molecular Biology (miscellaneous)


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