Interdependent evolutionary dynamics of opinion and strategy on two-layer networks

Opinion dynamics and evolutionary games are two pivotal fields in social dynamics, and the intricate interplay between them has great practical significance and becomes worthy of further exploration. In this work, we investigate the interdependent evolutionary dynamics of opinion and strategy on two-layer networks. On one layer, individuals exchange their viewpoints and update opinions. On the other layer, they play public goods games, and their decisions of whether to invest and how much to invest evolve over time. Based on different time scales as well as different interplay modes of the two dynamics, we consider three schemes, constant-opinion scheme, opinion-guided scheme and mutual-influence scheme. Our results show that the mutual-influence scheme, which incorporates both opinion attraction and opinion repulsion in opinion updating, facilitates the evolution of cooperation best among the three. By observing the distributions and the snapshots of opinions and strategies, we reveal that the heterogeneity in investment and the considerable amount of investment are two key factors contributed to the improvement of cooperation. These results illustrate the critical role that the interplay between opinion dynamics and strategic decision-making plays in addressing the real-world issues concerning collective behavior and resource allocation. Additionally, different convergence and divergence rates for opinion attraction and opinion repulsion in the mutual-influence scheme are considered. This study demonstrates that interdependent evolutionary dynamics of opinion and strategy can be employed to elucidate the intrinsic mechanisms of cooperation evolution and opinion formation.