Network-Based Phase Space Analysis of the El Farol Bar Problem

Area of Science:

• Complex Systems
• Agent-Based Modeling
• Game Theory

Background:

• The El Farol Bar problem illustrates bounded rationality, a scenario where agents make decisions with limited information.
• Previous analysis used high-dimensional phase spaces (N-1 dimensions) to visualize strategy distribution dynamics, posing visualization challenges.

Purpose of the Study:

• To develop a new, lower-dimensional method for visualizing and analyzing strategy dynamics in complex systems.
• To address the dimensionality limitations of previous phase space approaches for the El Farol Bar problem.

Main Methods:

• Converted strategy dynamics into a state transition network based on strategy distributions.
• Defined attractors of the strategy phase space as sink-strongly connected components within the network.
• Analyzed the resulting weighted, directed network to understand strategy performance.

Main Results:

• The state transition network provides a clearer representation of strategy dynamics compared to high-dimensional phase spaces.
• The network approach successfully visualizes attractors as sink-strongly connected components.
• This method simplifies the study of strategy performance in the El Farol Bar problem.

Conclusions:

• The proposed network approach effectively visualizes and analyzes complex system dynamics, overcoming dimensionality issues.
• This method is applicable to the El Farol Bar problem and other discretized complex systems.
• The network representation offers a powerful tool for understanding agent strategy evolution and system behavior.