标题： 高阶相互作用的进化博弈动力学 显示英文标题

标题： Evolutionary game dynamics for higher-order interactions

摘要： 协作行为深深嵌入在结构化的生物和社会系统中。 网络常用于描述个体之间的成对互动，其中网络节点代表个体，链接表示谁与谁互动。 然而，越来越多的人认识到，许多实证互动往往涉及三个或更多个体，而不是被大大简化的低阶成对互动，这突显了在理解不同规模个体数量的高阶互动中集体合作进化的根本差距。 在这里，我们开发了一个进化博弈动力学的理论框架，以系统地分析在高阶互动下合作如何进化并固定。 具体来说，我们提供了一个简单的条件，在任意不同阶次互动的组合下，合作都会被偏好。 与成对互动相比，我们的研究结果表明，高阶互动使得合作出现的阈值更低。 令人惊讶的是，我们展示了高阶互动在大规模系统中有利于合作的进化，这与低阶情况相反。 我们的结果为理解具有高阶互动的实证系统中的集体合作进化提供了新的途径。 显示英文摘要

摘要： Cooperative behaviors are deeply embedded in structured biological and social systems. Networks are often employed to portray pairwise interactions among individuals, where network nodes represent individuals and links indicate who interacts with whom. However, it is increasingly recognized that many empirical interactions often involve triple or more individuals instead of the massively oversimplified lower-order pairwise interactions, highlighting the fundamental gap in understanding the evolution of collective cooperation for higher-order interactions with diverse scales of the number of individuals. Here, we develop a theoretical framework of evolutionary game dynamics for systematically analyzing how cooperation evolves and fixates under higher-order interactions. Specifically, we offer a simple condition under which cooperation is favored under arbitrary combinations of different orders of interactions. Compared to pairwise interactions, our findings suggest that higher-order interactions enable lower thresholds for the emergence of cooperation. Surprisingly, we show that higher-order interactions favor the evolution of cooperation in large-scale systems, which is the opposite for lower-order scenarios. Our results offer a new avenue for understanding the evolution of collective cooperation in empirical systems with higher-order interactions.