The public goods game on scale-free networks with heterogeneous investment

Heterogeneity has received increasing attention over the past decade, and it is widely considered to have a great effect on promoting cooperation. In our paper, we investigate the influence of heterogeneous investment on the cooperative behavior of the system, which is based on the number of players in different groups in the evolutionary public goods game (PGG). A parameter α is used to tune the heterogeneous investment mechanism: if α>0, cooperators invest more in the groups centered on high-degree nodes, but if α<0, the groups centered on small-degree nodes attract more investment from cooperators. Simulation results and analysis suggest that the cooperation level is enhanced in a large range. For a smaller enhancement factor r in the PGG model, the cooperation frequency decreases monotonously with the increase of α. For a larger r, the highest cooperation level can only be obtained by α=0, which is a non-monotonous phenomenon. By investigating the mean payoffs of nodes of different degrees for different α, it is found that the strategy utilized by hubs is more prominent in the system. Some explanations are provided for the strategy orientation of hubs and show that the investment propensity will change it. Our work may be useful for understanding the influence of individual investment in different groups on the level of cooperation.