Abstract
Direct, indirect and network reciprocity are key mechanisms fostering cooperation in societies. Though intrinsically interrelated, they are often studied separately. Unravelling the evolutionary dynamics of reciprocity in structured populations remains challenging. Here, we develop a general model to explore the evolution of direct and indirect reciprocity on networks. Drawing on our model, we derive a simple rule for cooperation to evolve through reciprocity. Applying this rule to 1 million random networks, we investigate how network topology influences evolutionary outcomes. We find that, in general, direct reciprocity is easier to promote cooperation on these networks. Additionally, direct reciprocity remains robust when a population adapts to the environment through social learning. Notably, environmental fluctuations significantly lower the threshold for cooperation through indirect reciprocity. Overall, our work sheds light on a fresh framework for comprehending the evolution of reciprocity.
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