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Abstract

In a community-structured population, public goods games (PGG) occur both
within and between communities. Such type of PGG is referred as multilevel public goods games
(MPGG). We propose a minimalist evolutionary model of the MPGG and analytically study the
evolution of cooperation. We demonstrate that in the case of sufficiently large community size
and community number, if the imitation strength within community is weak, i.e., an individual
imitates another one in the same community almost randomly, cooperation as well as punishment
are more abundant than defection in the long run; if the imitation strength between communities
is strong, i.e., the more successful strategy in two individuals from distinct communities is always
imitated, cooperation and punishment are also more abundant. However, when both of the two
imitation intensities are strong, defection becomes the most abundant strategy in the population.
Our model provides insight into the investigation of the large-scale cooperation in public social
dilemma among contemporary communities.