Emergence of group cooperation through probabilistic guidance in repeated interactions

How to promote cooperation among irrelevant agents has long been a pressing challenge in multi-agent systems. Recent theoretical studies have revealed that group cooperation can be facilitated by actively guiding rule-breaking agents to adjust their behaviors. However, in the process of a single-game interaction, it seems unrealistic to convert all free-riders into cooperators through guidance, as there exist stubborn agents who are impervious to such guidance. In this work, we introduce a probabilistic guidance mechanism within the framework of repeated public goods games, and investigate the impact of peer guidance and pool guidance mechanisms on the evolution of cooperation. In the former, guiders incur costs to guide free-riders, while the latter relies on institutions to guide free-riders. We investigate replicator dynamics in infinite populations and stochastic dynamics in finite populations, respectively. We find that guidance in repeated interaction scenarios promotes the emergence of cooperation, and that guidance is more likely to succeed when the probability of guidance increases with the rise in guidance costs.