标题： 高阶策略更新促进合作的出现 显示英文标题

标题： Emergence of cooperation promoted by higher-order strategy updates

摘要： 合作是人类社会的基础，个体之间的互动结构深刻地塑造了合作的出现和演变。 在现实场景中，合作在多群体（高阶）人口中占主导地位，而不仅仅是二元行为。 尽管近年来对高阶网络中的群体困境进行了研究，但由于群体间互动的复杂性和不可分割性，由高阶策略更新驱动的合作探索仍然有限。 在这里，我们研究了公共物品游戏中策略更新的四种高阶机制，并建立了其合作出现的数学条件。 这些条件揭示了高阶策略更新和网络特性对进化结果的影响，特别强调了群体重叠对合作的促进作用。 有趣的是，我们发现一种策略机制，交替最优性和随机性——选择一个优秀的群体，然后在这个群体内模仿一个随机个体——可以显著促进合作。 我们的分析进一步揭示了与成对互动相比，高阶策略更新通常在大多数高阶网络中改善合作。 这些发现突显了高阶策略更新在复杂社会系统中促进集体合作的关键作用。 显示英文摘要

摘要： Cooperation is fundamental to human societies, and the interaction structure among individuals profoundly shapes its emergence and evolution. In real-world scenarios, cooperation prevails in multi-group (higher-order) populations, beyond just dyadic behaviors. Despite recent studies on group dilemmas in higher-order networks, the exploration of cooperation driven by higher-order strategy updates remains limited due to the intricacy and indivisibility of group-wise interactions. Here we investigate four categories of higher-order mechanisms for strategy updates in public goods games and establish their mathematical conditions for the emergence of cooperation. Such conditions uncover the impact of both higher-order strategy updates and network properties on evolutionary outcomes, notably highlighting the enhancement of cooperation by overlaps between groups. Interestingly, we discover that the strategical mechanism alternating optimality and randomness -- selecting an outstanding group and then imitating a random individual within this group -- can prominently promote cooperation. Our analyses further unveil that, compared to pairwise interactions, higher-order strategy updates generally improve cooperation in most higher-order networks. These findings underscore the pivotal role of higher-order strategy updates in fostering collective cooperation in complex social systems.