Cooperative behavior in two-layer networks with co-evolving relationships and reputation

This paper investigates how the interplay between dynamic relationships and reputation influences cooperative behavior. We propose an evolutionary game model on a two-layer network based on the prisoner’s dilemma, capturing the co-evolution of relationship structure, reputation, and strategy. The model includes a fixed network and a time-varying network, where dynamic links are formed through an activity-driven mechanism combining homophily and reputation attraction. A memory-based reputation updating rule with time decay is introduced to reflect realistic reputation dynamics. In addition, a preference parameter is used to describe individuals’ heterogeneous learning from fixed and dynamic interactions. Simulation results show that reputation-driven link rewiring promotes the formation of cooperative clusters and improves system robustness. Memory effects mainly influence cooperation indirectly by shaping reputation accumulation. Behavioral preference and payoff weighting act as key regulators connecting network structure and strategy evolution. Moreover, scale-free networks enhance the stability of cooperation and reputation compared to homogeneous networks and reduce sensitivity to parameter changes. Overall, the results highlight that the interaction between network structure and reputation is a key driver of cooperation, offering new insights into cooperative behavior in complex social systems.