We live and cooperate in networks. However, links in networks only allow for pairwise interactions, thus making the framework suitable for dyadic games, but not for games that are played in larger groups. Here, we study the evolutionary dynamics of a public goods game in social systems with higher-order interactions. First, we show that the game on uniform hypergraphs corresponds to the replicator dynamics in the well-mixed limit, providing a formal theoretical foundation to study cooperation in networked groups. Second, we unveil how the presence of hubs and the coexistence of interactions in groups of different sizes affects the evolution of cooperation. Finally, we apply the proposed framework to extract the actual dependence of the synergy factor on the size of a group from real-world collaboration data in science and technology. Our work provides a way to implement informed actions to boost cooperation in social groups.

我们在网络中生活和合作。然而，网络中的链接只允许成对交互，从而使该框架适用于二元游戏，但不适用于更大群体的游戏。在这里，我们研究了具有高阶交互的社会系统中公共物品博弈的演化动力学。首先，我们表明均匀超图上的博弈对应于混合均匀极限下的复制动力学，为研究网络群体中的合作提供了正式的理论基础。其次，我们揭示了枢纽的存在和不同规模群体中相互作用的共存如何影响合作的演变。最后，我们应用所提出的框架从现实世界的科学和技术协作数据中提取协同因子对群体规模的实际依赖性。