Evolutionary Dynamics of Group Cooperation on Heterogeneous Higher-Order Networks

Group cooperation is vital for the prosperity and development of human societies. Previous studies have demonstrated that network structures and their structural heterogeneities significantly affect the evolution of cooperation. Most of these studies focus on traditional networks, where edges represent pairwise interactions. However, interactions frequently go beyond pairwise connections, occurring within groups of varying sizes and exhibiting nonlinear effects. Higher-order networks capture such characteristics by allowing general group interactions among more than two individuals with hyperedges. Here, we explore the effect of degree heterogeneity and order (i.e., group size) heterogeneity on the evolution of cooperation under both linear public goods games (PGGs) and nonlinear multiplayer snowdrift games (MSGs). We find that compared with degree homogeneity, strong degree heterogeneity may inhibit the evolution of cooperation in public goods games whereas in multiplayer snowdrift games, it can instead confer additional benefits for cooperation. Moreover, our results show that order heterogeneity reduces the threshold for the evolution of cooperation in multiplayer snowdrift games while having an almost negligible impact on cooperation in public goods games. Through extensive simulations, we reveal that such differences result from the distinct payoff structures of these two games. Our work thus highlights that how structural heterogeneities of higher-order networks affect the evolution of cooperation depends on the specific games employed, and it is necessary to consider both linear and nonlinear games to uncover the intricate and unique effect of higher-order interactions on evolutionary outcomes.