集体风险公共品博弈中的分岔与多稳态：基于法定人数激活的保护机制
Bifurcation and Multistability in a Collective-Risk Public Goods Game with Quorum-Activated Protection
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- Yunnan University of Finance and Economics（云南财经大学）
- Kunming University（昆明学院）
- Institute of Technical Physics and Materials Science, Centre for Energy Research（匈牙利科学院技术物理与材料科学研究所能源研究中心）
机构由 AI 辅助整理，请以论文原文为准。
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中文总结 AI 辅助
本研究通过N人公共品博弈模型，发现保护性合作需在完成法定人数且收益超过成本时才能演化，且存在多稳态分岔，区分了保护有效性与稀有入侵能力。
中文摘要 AI 辅助
公共品博弈中集体风险的危险性可能为摆脱公地悲剧提供有效途径。现有研究通常将风险缓解嵌入贡献行为本身，而许多真实系统依赖于一种独立的、有成本且非排他性的保护活动，该活动需要参与法定人数。此类保护机制能否演化并持续存在仍不清楚。在此，我们构建了一个包含普通合作者、背叛者和保护性合作者的N人公共品博弈模型。背叛者内生地增加一个饱和的集体失败概率，而保护性合作者承担额外成本，且一旦其人数达到法定人数，便为所有群体成员降低此风险。复制者分析与数值分岔计算得出三项主要发现。第一，当焦点参与者完成法定人数且由此产生的预期损失减少超过其额外成本时，保护性合作获得优势。该优势随群体构成呈非单调变化。第二，当单个保护性合作者无法激活保护时，保护有效性不会进入其在完全背叛状态下的首阶入侵适应度；当完全背叛局部渐近稳定时，更高的有效性无法克服稀有入侵障碍。第三，边界鞍结分岔产生一个鞍点和一个局部渐近稳定的背叛者与保护性合作者共存平衡点。当完全合作与完全背叛也局部渐近稳定时，三个吸引子共存，数值观察到的演化结果取决于初始群体构成。这些结果区分了激活保护的有效性与其从稀有状态建立的能力。
英文摘要
The danger of collective risk in a public goods game could provide an effective escape route from the tragedy of the commons. Existing studies usually embed risk mitigation in the contribution itself, whereas many real systems rely on a separate costly and non-excludable protective activity that requires a participation quorum. Whether such protection can evolve and persist remains unclear. Here, we formulate an $N$-player public-goods game with ordinary cooperators, defectors, and protective cooperators. Defectors endogenously increase a saturating probability of collective failure, whereas protective cooperators incur an additional cost and reduce this risk for all group members once their number reaches the quorum. Replicator analysis and numerical bifurcation calculations yield three main findings. First, protective cooperation gains an advantage when the focal participant completes the quorum and the resulting expected loss reduction exceeds its additional cost. This advantage varies non-monotonically with group composition. Second, when a single protective cooperator cannot activate protection, protection effectiveness does not enter its first-order invasion fitness at full defection; greater effectiveness cannot overcome the rare-invasion barrier when full defection is locally asymptotically stable. Third, a boundary saddle--node bifurcation creates a saddle and a locally asymptotically stable coexistence equilibrium of defectors and protective cooperators. When full cooperation and full defection are also locally asymptotically stable, three attractors coexist, and the numerically observed evolutionary outcome depends on the initial population composition. These results distinguish the effectiveness of activated protection from its ability to become established from rarity.
