The rise and fall of cooperation in populations with multiple groups

Abstract

It is a challenge to understand why cooperation is prevalent in human society, especially without a mechanism that benefits cooperators such as direct, indirect and strong reciprocity. We study an evolutionary process of public goods game among individuals in multiple groups in a population. We find that the existence of an independent cooperator group is beneficial to the rise of cooperation in the population, which is applicable to both Moran process and a so-called disaster update process proposed in this paper. However, the introduction of mutation can completely overturn the emerging trend of cooperation, and even let the defectors occupy the whole population for a short period of time, by continuously reducing the number of cooperator groups. In addition, the migration of individuals between groups can also inhibit cooperation. More specifically, a higher frequency of migration can reduce the probability of cooperators occupying the population, and extend the time it takes for the population to reach the stationary state. Furthermore, we find that a special kind of multi-individual migration, namely group division, can resist the anti-cooperation effect of mutation to some extent, mainly by maintaining a certain number of cooperator groups in the population. The aforementioned results suggest that cooperation can rise without strengthening the ability of cooperators to directly confront the defectors in a population composed of multiple groups.