The El Farol Bar problem is a game theory problem where actors must decide whether or not to go to a bar with limited information. We recently proposed to study this problem as a dynamical system of strategy distribution space and revealed its dynamics and attractors in this phase space [1]. However, the previous research was limited in that the phase space required N-1 dimensions to fully visualize where N is the number of decision strategies. To address this issue, here we propose a novel phase space visualization and analysis method that converts the dynamics of the strategy distribution with any number of decision strategies into a weighted directed network. Each node represents a unique distribution of strategies and each edge represents an observed state change from one distribution to another (Fig. 1a). The edge weight indicates the number of times the transition occurred in all simulations. This network-based representation of the strategy dynamics lets us identify an attractor in the strategy phase space as a strongly connected component with no outgoing edges. The entire phase space topology can also be systematically investigated using various other network analysis tools. We found power law relationships in the node degree (strength) distribution (Fig. 1b) and the edge weight distribution, which manifest more when the number of strategies increases. Furthermore, this approach not only provides a generalized analysis of the El Farol Bar Problem as a dynamical system but is problem-agnostic and can be applied to any high-dimensional discretized dynamical systems.
