False beliefs can bootstrap cooperative communities through social norms.

Building cooperative communities is a crucial problem for human societies. Much research suggests that cooperation is facilitated by knowing who the cooperators and defectors are, and being able to respond accordingly. As such, anonymous games are thought to hinder cooperation. Here, we show that this conclusion is altered dramatically in the presence of conditional cooperation norms and heterogeneous beliefs about others' behaviours. Specifically, we show that inaccurate beliefs about other players' behaviours can foster and stabilise cooperation via social norms. To show this, we combine a community's population dynamics with the behavioural dynamics of their members. In our model, individuals can join a community based on beliefs generated by public signals regarding the level of cooperation within, and decide to cooperate or not depending on these beliefs. These signals may overstate how much cooperation there really is. We show that even if individuals eventually learn the true level of cooperation, the initially false beliefs can trigger a dynamic that sustains high levels of cooperation. We also characterise how the rates of joining, leaving and learning in the community affect the cooperation level and community size simultaneously. Our results illustrate how false beliefs and social norms can help build cooperative communities.