Impact of heterogeneous network structures on the evolution of group behavior

This study systematically examines how complex network architectures and their transitional forms influence cooperative evolution in populations characterized by coexistence of cooperation diversity and strategy persistence. Through comparative analysis of regular ring networks, small-world (SW) networks, Erdös–Rényi (ER) random networks, scale-free (SF) networks, and their structural transitions, we reveal significant parameter-dependent variations in cooperation levels. The structural progression from regular rings to SW and subsequently to ER networks demonstrates a general enhancement of average cooperation tendency with increasing rewiring probability, interrupted by a characteristic dip in cooperator fraction during the SW-to-ER transition. Remarkably, the ER-to-SF network evolution initially elevates cooperation to universal cooperation before hub agents develop preferences for high but incomplete cooperation levels, paradoxically reducing the population-wide average cooperation tendency while preserving full cooperation prevalence. These counterintuitive phenomena are attributed to cooperation diversity’s dual role. It amplifies cooperation in regular networks while enabling extreme strategy adoption in SW wised networks, and induces strategic moderation among SF network hubs. Our findings are independent of the selection intensity and highlight how network topology transitions nonlinearly reshape cooperative dynamics under the cooperation diversity introduction through structural constraints on agent interactions and heterogeneous connectivity patterns.