发表机构
The College of Artificial Intelligence, Southwest University; Business College, Southwest University; Department of Complexity Science, Potsdam Institute for Climate Impact Research; Institute of Physics, Humboldt University of Berlin; Institute of Technical Physics and Materials Science, Centre for Energy Research（西南大学人工智能学院; 西南大学商学院; 波茨坦气候影响研究所复杂性科学系; 柏林洪堡大学物理研究所; 匈牙利能源研究中心技术物理与材料科学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究将社会比较理论引入结构化种群的演化动力学，发现比较参数非线性改变合作临界条件，并识别出异质但整体同化的最优比较模式，为设计促进合作的社会激励提供依据。
AI 中文摘要
人类合作发生在其社会环境中，个体通过基于收益的学习和社会比较（即相对于他人评估自身适应度的倾向）相互影响。然而，社会比较和种群结构如何共同塑造合作仍不清楚。在此，我们将社会比较理论纳入结构化种群上的演化动力学，使适应度取决于由比较参数加权的个体和邻居收益。在弱选择下，我们推导出有利于合作的条件，并发现所提出的比较非线性地重塑了临界收益-成本比。即使一个个体应用该协议也能影响整个种群，尤其是在异质网络中。当比较倾向变化时，完整的分布（而不仅仅是均值）决定演化结果。利用基于群体智能的框架在典型和经验网络中，我们识别出合作最大化的模式：最优状态表现出异质的比较倾向，但总体上趋向于同化发展。这些结果为设计利用比较来促进人类群体集体合作的社会激励提供了基础。
英文摘要
Human cooperation unfolds in social environments where individuals influence each other through payoff-based learning and social comparison, the tendency to evaluate fitness relative to others. However, it is still unclear how social comparison and population structure jointly shape cooperation. Here, we incorporate social comparison theory into evolutionary dynamics on structured populations, letting fitness depend on individual and neighbour payoffs weighted by a comparison parameter. Under weak selection, we derive conditions favoring cooperation and find that the proposed comparison nonlinearly reshapes the critical benefit-to-cost ratio. Even one individual applying this protocol can affect the population, especially in heterogeneous networks. When comparison tendencies vary, the full distribution, not just the mean, determines evolutionary outcomes. Using a swarm-intelligence-based framework across typical and empirical networks, we identify cooperation-maximizing patterns: optimal states exhibit heterogeneous comparison tendencies, yet collectively align toward assimilative development. These results provide a basis for designing social incentives that harness comparison to promote collective cooperation in human groups.
