  Cooperation is one of the foundations of human society. Many solutions to
cooperation problems have been developed and culturally transmitted across
generations. Because immigration can play a role in nourishing or disrupting
cooperation in societies, we must understand how the newcomers' culture
interacts with the hosting culture. Here, we investigate the effect of
different acculturation settings on the evolution of cooperation in spatial
public goods games with the immigration of defectors and efficient cooperators.
Here, immigrants may be socially influenced, or not, by the native culture
according to four acculturation settings: integration, where immigrants imitate
both immigrants and natives; marginalization, where immigrants do not imitate
either natives or other immigrants; assimilation, where immigrants only imitate
natives; and separation, where immigrants only imitate other immigrants. We
found that cooperation is greatly facilitated and reaches a peak for moderate
values of the migration rate under any acculturation setting. Most
interestingly, we found that the main acculturation factor driving the highest
levels of cooperation is that immigrants do not avoid social influence from
their fellow immigrants. We also show that integration may not promote the
highest level of native cooperation if the benefit of cooperation is low.
