Prosocial behaviours are encountered in the donation game, the prisoner’s dilemma, relaxed social dilemmas and public goods games. Many studies assume that the population structure is homogeneous, meaning that all individuals have the same number of interaction partners or that the social good is of one particular type. Here, we explore general evolutionary dynamics for arbitrary spatial structures and social goods. We find that heterogeneous networks, in which some individuals have many more interaction partners than others, can enhance the evolution of prosocial behaviours. However, they often accumulate most of the benefits in the hands of a few highly connected individuals, while many others receive low or negative payoff. Surprisingly, selection can favour producers of social goods even if the total costs exceed the total benefits. In summary, heterogeneous structures have the ability to strongly promote the emergence of prosocial behaviours, but they also create the possibility of generating large inequality.

在捐赠游戏，囚徒困境，放松的社会困境和公益游戏中会遇到亲社会行为。许多研究假设人口结构是同质的，这意味着所有个体具有相同数量的互动伙伴，或者社会福利属于一种特定类型。在这里，我们探讨了任意空间结构和社会商品的一般进化动力学。我们发现，异构网络中的某些人比其他人具有更多的交互伙伴，可以促进亲社会行为的发展。但是，他们通常会在少数关系密切的人手中积累大部分收益，而其他许多人则得到的收益很低或为负。出人意料的是，即使总成本超过总收益，选择也会有利于社会商品的生产者。综上所述，