Evolutionary Games On Visibility Graphs

We show that time series of different complexities can be transformed into networks that host individuals playing evolutionary games. The irregularity of the time series is thereby faithfully reflected in the fraction of cooperators surviving the evolutionary process, thus effectively linking time series with evolutionary games. Pivotal to the linkage is a simple visibility algorithm that transforms time series into networks. More specifically, periodic series yield regular networks, chaotic series yield random networks, while fractal series yield scale-free networks. As an example, we use a chaotic time series from the Logistic map and a fractal time series of Brownian motion, yielding an interaction network with an exponential and a power-law degree distribution, respectively. By employing the prisoner's dilemma and the snowdrift game, we demonstrate that such heterogeneous interaction networks facilitate the evolution of cooperation if compared to the traditional square lattice topology. Due to the simplicity of the employed methodology, newcomers with a basic command of nonlinear dynamics or stochastic processes can become easily acquainted with evolutionary games, and moreover, integrate these interesting and vibrant subfields of physics more effectively into their research.