The impact of heterogeneous interpersonal relationships on promoting cooperation under the reputation mechanisms in public goods game.

Although the principle of "case-by-case analysis" is widely endorsed, achieving complete rationality in the real world continues to be fraught with difficulties. Interpersonal relationships are heterogeneous, and the influence of social relationships and worldly wisdom on reputation evaluation should not be overlooked. Therefore, based on indirect reciprocity theory, this paper constructs a public goods game model with strategy update rules driven by reputation mechanism, aiming to investigate the impact of heterogeneous interpersonal relationships on the promotion of cooperative public goods provision among residents. The paper categorizes interpersonal relationships into three types, and proposes three corresponding reputation evaluation rules. Simulation results demonstrate that varying intensities of interpersonal relationships result in different levels of cooperation. When conducting public activities, externalities and the organizational efficiency of managers must be considered. Meanwhile, cooperation is difficult to sustain if the reputation mechanism fails to function effectively.