Evolutionary dynamics of cooperation in two-layer lattice networks with a leader-follower hierarchy: integrating dominant strategy and time cost

This study explores the evolution of cooperative behavior in two-layer lattice networks by introducing time cost and a dominant-strategy mechanism within a leader-follower hierarchy network framework. The findings reveal that time cost acts as a stabilizer for system-wide cooperation, effectively mitigating the inhibitory effect of high cooperation costs. Meanwhile, the dominant-strategy mechanism provides clear behavioral references for the follower layer, significantly enhancing cooperation both within individual layers and across the entire network. Numerical simulations demonstrate that the follower layer exhibits higher cooperative synergy under the cooperation-dominant mechanism, whereas the cooperation level in the leader layer is instead enhanced under the defection-dominant mechanism. The study further shows that parameters such as selection intensity, consistency incentives, and inter-layer coupling strength all promote the emergence of cooperation under specific conditions. This work provides a mechanistic explanation and analytical tools for the evolution of cooperation in hierarchical social structures.