Evolutionary dynamics of asymmetric trust games on weighted scale-free networks

Trust is a fundamental mechanism for maintaining social order, and its evolutionary dynamics have long been an interdisciplinary topic in the field of network and social sciences. Previous studies on trust games have largely relied on network-based simulations and have rarely considered the heterogeneity of edge weights. In this work, we investigate the evolutionary dynamics of investors and trustees on weighted heterogeneous networks, emphasizing the combined effects of network structure, weighting mechanisms, and payoff–punishment parameters on trust formation. We model interactions between investors and trustees using a four-dimensional nonlinear dynamical system, and then perform linear stability analysis to characterize the strategy evolution. The results reveal heterogeneous and hierarchical investment diffusion, where low-degree nodes adopt investment strategies earlier and drive local trust formation, while high-degree nodes are primarily influenced by network adjacency and weight effects. Moreover, parameters such as the average degree 〈k〉, network heterogeneity exponent γ, trustee proportion α, and trustworthy multiplication factor RT collectively determine the investment threshold. Numerical simulations validate the theoretical findings and demonstrate equilibrium states with full investment and partial trust. Current results highlights the critical role of network heterogeneity and edge weights in sustaining trust and cooperation in networked systems.