  Previous research has highlighted the importance of strong heterogeneity for
the successful evolution of cooperation in games governed by pairwise
interactions. Here we determine to what extent this is true for games governed
by group interactions. We therefore study the evolution of cooperation in the
public goods game on the square lattice, the triangular lattice and the random
regular graph, whereby the payoffs are distributed either uniformly or
exponentially amongst the players by assigning to them individual scaling
factors that determine the share of the public good they will receive. We find
that uniformly distributed public goods are more successful in maintaining high
levels of cooperation than exponentially distributed public goods. This is not
in agreement with previous results on games governed by pairwise interactions,
indicating that group interactions may be less susceptible to the promotion of
cooperation by means of strong heterogeneity as originally assumed, and that
the role of strongly heterogeneous states should be reexamined for other types
of games.
