Evolutionary dynamics of trust in hierarchical populations with varying investment strategies

Trust is one of the fundamental elements in the development of human societies, which can be modelled on the trust game. In the traditional trust game, investors decide whether to invest or not, and trustees choose whether to be trustworthy or not. In this study, we differentiate between investors and trustees and assume that strategy imitation only happens among individuals of the same class, in which their ratios remain constant. Trustees can choose to be either trustworthy or untrustworthy, while investors decide between an active and a conservative investment strategies based on environmental factors. Here, the environmental factor is closely related to the number of trustworthy trustees within the group. Applying evolutionary game theory, we investigate behavioural changes in the [Formula: see text]-player trust game when environmental factors are introduced. Our findings indicate that investors can form effective coalitions with trustworthy trustees, thereby excluding untrustworthy ones. Furthermore, we validate the robustness of our model and reveal that different investment behaviours have different advantages under specific environmental conditions. This study highlights the subtle interplay between trust and investment dynamics in different environments, providing new insights into the mechanisms of trust in socioeconomic systems, which has some practical significance.