Understanding how cooperative behaviours can emerge from competitive interactions is an open problem in biology and social sciences. While interactions are usually modelled as pairwise networks, the units of many real-world systems can also interact in groups of three or more. Here, we introduce a general framework to extend pairwise games to higher-order networks. By studying social dilemmas on hypergraphs with a tunable structure, we find an explosive transition to cooperation triggered by a critical number of higher-order games. The associated bistable regime implies that an initial critical mass of cooperators is also required for the emergence of prosocial behavior. Our results show that higher-order interactions provide a novel explanation for the survival of cooperation.

翻译：理解合作行为如何从竞争性相互作用中涌现，是生物学与社会科学中的一个悬而未决的问题。虽然相互作用通常被建模为成对网络，但许多现实世界系统的单元也可能以三个或更多成员的群体形式互动。在此，我们提出一个通用框架，将成对博弈扩展至高阶网络。通过研究具有可调结构的超图上的社会困境，我们发现由临界数量的高阶博弈触发的向合作的爆发式转变。伴随的双稳态机制表明，亲社会行为的出现还需要初始的临界合作者群体。我们的研究结果表明，高阶相互作用为合作存续提供了新的解释。