D. Y. Wang, Peng Yi, Gang Yan, Feng Fu
Understanding how cooperation evolves in structured populations remains a fundamental question across diverse disciplines. The problem of cooperation typically involves pairwise or group interactions among individuals. While prior studies have extensively investigated the role of networks in shaping cooperative dynamics, the influence of tie or connection strengths between individuals has not been fully understood. Here, we introduce a quenched mean-field based framework for analyzing both pairwise and group dilemmas on any weighted network, providing interpretable conditions required for favoring cooperation. Our theoretical advances further motivate us to find that the degree-inverse weighted social ties – reinforcing tie strengths between peripheral nodes while weakening those between hubs – robustly promote cooperation in both pairwise and group dilemmas. Importantly, this configuration enables heterogeneous networks to outperform homogeneous ones in fixation of cooperation, thereby adding to the conventional view that degree heterogeneity inhibits cooperative behavior under the local stochastic strategy update. We further test the generality of degree-inverse weighted social ties in promoting cooperation on$30, 000$random networks and 13 empirical networks drawn from real-world systems. Finally, we unveil the underlying mechanism by examining the formation and evolution of cooperative ties under social ties with degree-inverse weights. Our systematic analyses provide new insights into how the network adjustment of tie strengths can effectively steer structured populations toward cooperative outcomes in biological and social systems.