Environmental heterogeneity unifies the effect of spatial structure on the altruistic cooperation in game-theory paradigms

As vivid metaphors for social dilemmas, the prisoner's dilemma game, snowdrift game, and stag hunt game have been the focus of game theory research. Incorporating spatial structure into game models has been proven to have the opposite impact on the evolution of cooperation. Nevertheless, it is demonstrated here that spatial structure always fosters cooperation provided the environmental heterogeneity is included, regardless of the social dilemma. We consider the static and dynamic heterogeneous environment categories. The results exhibit that, in a static environment with two state types (poor and rich), a higher quality level of the rich state can bring a more pronounced improvement effect, and a moderate proportion of the rich-type environment will enable the density of cooperators to reach its maximum. To portray a more realistic scenario, the state types are further increased to fulfill the uniform distribution and the normal distribution, respectively, meanwhile they are allowed to fluctuate. It is shown that the enhancement effect is invariably verified. Additionally, the uniform distribution performs better in the static environment while two distributions present virtually consistent impact in the dynamic environment. The robustness analysis reveals that our claims are supported under various initial distributions, environment compositions, population configurations, and even the heat maps of parameter combination T-S. Our conclusions imply that environmental heterogeneity is crucial to the development of cooperation in social dilemmas.