Clarifying social norms which have robustness against reputation costs and defector invasion in indirect reciprocity

The evolution of cooperation through indirect reciprocity is a pivotal mechanism for sustaining large-scale societies. Because third parties return cooperative behaviour in indirect reciprocity, reputations that assess and share these third parties' behaviour play an essential role. Studies on indirect reciprocity have predominantly focused on the costs associated with cooperative behaviour, overlooking the costs tied to the mechanisms underpinning reputation sharing. Here, we explore the robustness of social norms necessary to secure the stability of indirect reciprocity, considering both the costs of reputation and the resilience against perfect defectors. Firstly, our results replicate that only eight social norms, known as the 'leading eight,' can establish a cooperative regime. Secondly, we reveal the robustness of these norms against reputation costs and perfect defectors. Our analysis identifies four norms that exhibit resilience in the presence of defectors due to their neutral stance on justified defection and another four that demonstrate robustness against reputation costs through their negative evaluation of unjustified cooperation. The study underscores the need to further research how reputational information is shared within societies to promote cooperation in diverse and complex environments.