  Indirect reciprocity unveils how social cooperation is founded upon moral
systems. Under the frame of dyadic games based on individual reputations, the
"leading-eight" social norms distinguish themselves in promoting and sustaining
cooperation. However, in real societies, people constantly interact within
larger groups. They are assessed not only by their own behaviors, but also the
reputations of the groups they come from and interact with. Here, we study
indirect reciprocity in public goods games with group reputations. We show that
varying criteria of group reputation assessment destabilize the consensus
within leading-eight populations. We find the presence of an optimal,
moderately set social assessment criterion that is most conductive to promoting
cooperation. As the payoff of group cooperation increases, the assessment
criterion evolves to relaxation following two dynamical patterns, indicating
that social prosperity encourages people to be tolerate. Our work identifies
the role of group reputation assessment to boost cooperation in social
populations.
