Network, direct and indirect reciprocity are three widely recognized mechanisms driving and sustaining cooperation, and each one of them is well understood when acting alone. However, these forms of reciprocity are barely found to be isolated from one another in the real circumstances, and it is still unclear which is the specific role played by each form of reciprocity works when they take action in parallel. With a unique data set from online societies, we find that direct and indirect reciprocity are actually moderated by network reciprocity. On the one hand, the cooperation boosting effect of direct and indirect reciprocity is stronger when subjects have more social connections, indicating that network reciprocity facilitates the formation of direct and indirect reciprocal interactions. On the other hand, this effect declines dramatically for upstream indirect reciprocity (also known as generalized reciprocity) and completely disappears for downstream indirect reciprocity (regarding reputation) when social connections are absent, indicating that social links is a pivotal factor in transmitting gratitude and building reputation. Our study deepens, therefore, the understanding of simultaneous effects of different mechanisms on the evolution of cooperation, and provides a fresh framework for empirically disentangling the factors of cooperative actions in real-world networks.
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