Coevolution of strategic behavior and opinion dynamics under heterogeneous influence on two-layer networks

The co-evolution of strategic behavior and opinion dynamics in structural groups is a key issue in social physics and evolutionary game theory. This study presents a new two-layer networks model to explore how asymmetric social influences between different social classes (polarized elite class and moderate public class) affect cooperation emergence and collective opinion formation. The model combines the public goods game with the bounded confidence opinion dynamics model. The upper layer has a polarized, bimodal opinion distribution, and the lower layer initially has a mild, unimodal distribution. A top-down coupling mechanism is introduced: a small number of low-level agents update viewpoints by combining upper-level peers’ views with a coupling strength, and transform strategy update rules from benefit-based imitation to opinion-driven random strategy adoption. Through Monte Carlo simulations, the coupled probability is scanned and its impact on two-layer stationary cooperative frequency and average opinion is analyzed. Results show a non-monotonic relationship between interlayer influence and cooperative outcomes. Moderate coupling can use elite opinions to enhance public-layer cooperation, while excessive coupling may cause opinion polarization and cascade, harming collective action stability. This work offers a computational framework for understanding complex interactions in multi-level social systems.