Pink-noise dynamics in an evolutionary game on a regular graph

TL;DR

This study investigates pink-noise dynamics in an evolutionary multiplayer prisoner's dilemma game on regular graphs, revealing complex correlation patterns and proposing a simple model to replicate observed behaviors.

Contribution

It introduces a novel analysis of pink-noise phenomena in evolutionary games on graphs and proposes a modified random-walk model to explain these dynamics.

Findings

Pink-noise behavior observed in the mixed cooperator-defector region.

Correlation between neighbors is enhanced in the mixed region.

A modified random-walk model reproduces pink-noise and deviations at low frequencies.

Abstract

We consider an iterated multiplayer prisoner's dilemma game on a square lattice and regular graphs based on the pairwise-Fermi update rule, and obtain heat-maps of the fraction of cooperators and the correlation of neighboring pairs. In the heat-map, there is a mixed region where cooperators and defectors coexist, and in the mixed region the correlation between neighbors is enhanced. Moreover, we observe pink-noise behavior in the mixed region, where the power spectrum can be fitted by a power-law function of frequency. We also find that the pink-noise behavior can be reproduced in a simple random-walk model. In particular, we propose a modified random-walk model which can reproduce not only the pink-noise behavior but also the deviation from it observed in a low-frequency region.