  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.
