具有结构意识的模仿动力学在高阶网络中
A unified framework for imitation dynamics on higher-order networks
AI总结：
本文提出了一种结构意识的模仿规则，用于在高阶网络中促进合作，通过信息多样性度量标准提升合作效果。
摘要：
模仿是结构化群体中策略进化的基本更新机制，决定了个体如何采样社会信息并将其转化为行为变化。高阶网络，如超图，将成对链接推广到超边，提供了群体互动的自然表示。然而，现有对高阶网络的研究大多强调结构效应，而基于模仿的更新规则的影响以及它们如何与群体结构相互作用仍不为人知。在此，我们引入了一类在超图上的结构意识模仿规则，明确参数化了被采样的群体数量以及在每个采样群体中咨询的同伴数量。在弱选择下，我们推导出在同质超图上任何多玩家社会困境中合作成功的解析条件。这一分析产生了一个可解释的度量标准，信息多样性，它量化了更新规则如何在群体间多样化社会信息的来源。解析预测和数值模拟显示，对于三个代表性困境，诱导更高信息多样性的更新规则更有效地促进合作。进一步的模拟显示，这一原则扩展到非同质超图和广泛类别的多玩家社会困境。我们的工作因此提供了一个统一的度量标准，将微观更新与进化结果联系起来，在高阶网络系统中建立了促进合作的一般设计原则，超越了成对互动。
英文摘要：
Cooperation is central to human societies and often unfolds within groups. Higher-order networks, such as hypergraphs, naturally represent these groups as hyperedges. Network structures and update rules, by which individuals revise their strategies, are the two fundamental components that shape the evolution of cooperation in structured populations. Yet while the effects of network structure have been studied extensively, update rules have been examined mostly through isolated models, leaving their relationships and the origins of their differing evolutionary outcomes poorly understood. Here we develop a unified framework for imitation dynamics on higher-order networks, parameterizing imitation-based update rules by the number of groups an individual samples and the number of peers consulted within each group. Under weak selection, we derive a closed-form condition for the success of cooperation in any multiplayer social dilemma on homogeneous hypergraphs, encompassing games with both linear and nonlinear payoff structures. The framework places previously disconnected update rules within a single family and reduces their effects on cooperation to one interpretable quantity, which we term information diversity. Update rules inducing higher information diversity promote cooperation more effectively, and we prove that this ordering holds strictly across the entire space of multiplayer social dilemmas. Simulations extend this principle to heterogeneous hypergraphs constructed both synthetically and from empirical data. Our framework provides a systematic way to represent, analyze, and compare update rules on higher-order networks, turning a fragmented collection of microscopic updating mechanisms into a tractable and interpretable theory.
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