  We study the evolution of cooperation in public goods games on different
regular graphs as a function of the noise level underlying strategy adoptions.
We focus on the effects that are brought about by different group sizes of
public goods games in which individuals participate, revealing that larger
groups of players may induce qualitatively different behavior when approaching
the deterministic limit of strategy adoption. While by pairwise interactions an
intermediate uncertainty by strategy adoptions may ensure optimal conditions
for the survival of cooperators at a specific graph topology, larger groups
warrant this only in the vicinity of the deterministic limit independently from
the underlying graph. These discrepancies are attributed to the indirect
linkage of otherwise not directly connected players, which is brought about by
joint memberships within the larger groups. Thus, we show that increasing the
group size may introduce an effective transition of the interaction topology,
and that the latter shapes the noise dependence of the evolution of cooperation
in case of pairwise interactions only.
