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| 热力学极限理论视角下间接互惠量子雪堆博弈合作行为研究 |
| Research on the cooperative behavior of indirect reciprocal quantum snowdrift game from the perspective of thermodynamic limit theory |
| 投稿时间：2025-08-29 修订日期：2026-02-13 |
| DOI： |
| 中文关键词: 热力学极限 磁化强度 Ising模型 间接互惠 量子雪堆博弈 |
| 英文关键词: thermodynamic limit magnetization Ising model indirect reciprocity quantum snowdrift game |
| 基金项目:教育部人文社会科学规划资助项目“量子博弈视角下寡头垄断企业均衡策略的复杂性机理及应用研究”(21YJA630116)；辽宁省教育厅基本科研资助项目“高维数据下竞争风险模型的变量选择方法研究”(LJKMZ20221412) |
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| 中文摘要: |
| 针对量子雪堆博弈中参与人数量无穷大时的合作行为问题，运用热力学极限理论，将一维Ising模型与一般两人博弈模型交叉融合，构建了间接互惠下的量子雪堆博弈模型，通过磁化强度刻画了量子雪堆博弈合作行为的动态演化特征，分析了纠缠度和辨别度对磁化强度的影响，并通过数值模拟得出：纠缠度和辨别度可有效地促进合作行为的涌现，当纠缠度和辨别度分别大于某一阈值时，磁化强度为正，多数人选择合作行为，此结论为解决大规模群体雪堆博弈出现的“囚徒困境”提供了一定决策理论依据。 |
| 英文摘要: |
| Regarding the problem of cooperative behavior in the quantum snowdrift game with an infinite number of participants, this study integrates the one-dimensional Ising model with the general two-player game model by the thermodynamic limit theory, sets up a quantum snowdrift game model under indirect reciprocity. The magnetization intensity is used to characterize the dynamic evolutionary features of cooperative behavior in the quantum snowdrift game model, the effects of entanglement degree and discrimination degree on magnetization intensity are analyzed, and numerical simulations are carried out. The results show that both entanglement degree and discrimination degree can effectively promote the emergence of cooperative behavior. When the entanglement degree and discrimination degree exceed certain thresholds, the magnetization intensity becomes positive, indicating that the majority of participants choose cooperative behavior. This conclusion offers a theoretical decision-making basis for addressing the "prisoner’s dilemma" in large-scale group snowdrift games. |
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