Field experiments with asymmetric commons dilemmas have shown that groups who are able to derive high social efficiency also had higher equity compared to groups who were not able to derive significant levels of social efficiency. These findings resemble the high productivity in long-lasting irrigation systems based on self-governance. We present an agent-based model based on cultural group selection that shows that the patterns observed in the field experiments can be evolved in cases where agents participate regularly in less challenging symmetric public good dilemmas. These results indicate that cooperation in asymmetric dilemmas can evolve and persist when the agents contend with other social dilemmas than the asymmetric dilemmas.