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.

When do societies succeed in providing public goods? Previous research suggests that public goods contributions correlate with expectations about cooperation by others among students and other demographic subgroups. However, we lack knowledge about whether the effect of expected cooperation is causal and a general feature of populations. We fielded representative surveys (N = 8,500) in France, Germany, the United Kingdom, and the United States that included a public goods game and a novel between-subjects experiment. The experiment varied expectations about cooperation by others. We find that higher expected cooperation by others causes a significant increase in individual contributions. When classifying contribution schedules, we find that almost 50% of the population employs a conditionally cooperative strategy. These individuals are on average richer, younger, and more educated. Our results help explain the varying success of societal groups in overcoming cooperation problems and assist policymakers in the design of institutions meant to solve social dilemmas.