Degree-dependent learning and teaching activities shape cooperation in scale-free networks

In social systems, a highly connected individual may be cautious in changing their own behavior, while still influencing many others through shared actions or information. This distinction reflects two different roles in behavioral updating: adopting behaviors from others and transmitting behaviors to others. Motivated by this observation, we study the Prisoner’s Dilemma on BA networks and develop a degree-dependent behavioral updating framework in which node degree is coupled separately with learning activity and teaching activity. Learning activity controls the tendency of individuals to adopt behaviors from neighbors, whereas teaching activity controls the ability of individuals to transmit their own behaviors to neighbors. Numerical simulations show that these two forms of activity generate contrasting effects on cooperation. When activity regulates learning, cooperation is promoted when nodes with high-degree have reduced activity, because this helps stabilize cooperative behavior on structurally important nodes. In contrast, when activity regulates teaching, cooperation is favored when nodes with high degree retain the standard activity level, because this supports the outward transmission of cooperative behavior. Further analyses of degree based cooperation profiles, cooperator clusters, and phase diagrams show that these patterns are robust and are closely related to the dual role of highly connected nodes in behavioral adoption and behavioral transmission. These results suggest that network heterogeneity affects cooperation not only through interaction structure, but also through the way structural position is translated into behavioral updating activity.