The spatial public goods game on hypergraphs with heterogeneous investment

The emergence of cooperation in the multi-person social dilemma has been extensive investigated under the pairwise interactions-based spatial public goods game (PGG). However, higher-order in-teractions are more suitable to describe the group relationships in real society and have attracted intensive interests. In this work, we propose an extension of the spatial PGG on hypergraphs, where cooperators are allowed to allocate their investments unevenly. A tunable parameter, a, is introduced to characterize the investment preference. a > 0 means that cooperators will allo-cate more investment to the PGG group from which they obtain higher payoff, while for a < 0, cooperators will allocate more investment to the group from which they gain lower payoff. Re-sults from numerical simulations indicate that compared with the results of homogeneous case, allocating more resources to profitable groups can effectively promote cooperation. Additionally, for a relative high synergy factor r, there exists a moderate negative value of a that will induce the lowest cooperation level, larger or smaller values of a can enable a higher cooperation level relative to the worst result. Moreover, the nontrivial results are robust against hypergraphs with different orders.

Automated summary

This research extends the spatial PGG on hypergraphs and allows cooperators to allocate investments unevenly. The results show that allocating more resources to profitable groups can effectively promote cooperation. Additionally, a moderate negative value of investment preference leads to the lowest level of cooperation.