Strategy persistence-consistency and reputation promote cooperation in dual-layer networks for prisoner’s dilemma games

We propose a dual-layer network model that integrates social and familial contexts, consisting of a social interaction layer and a family relationship layer. We design a reputation-based incentive mechanism incorporating strategy persistence-consistency to investigate how reputation fosters cooperation. The model features the following aspects: (1) a dynamic disconnection–reconnection mechanism in the social layer, (2) a reputation-enhanced Fermi rule in the family layer, and (3) a refined partitioning of the family network. Simulation results indicate that the disconnection–reconnection parameter (σ) significantly enhances cooperation in the social network; the strategic persistence-consistency influencing factor (α) has a positive impact on cooperation in both layers; and moderately dividing the family network promotes the emergence of cooperation. The research findings facilitate group cooperation in complex networks and offer valuable insights for addressing social dilemmas in the real world.