AI 中文总结
研究具有频率依赖回报的公共物品博弈中的进化动力学，引入一般频率依赖倍增因子，通过理论分析得出合作占优条件，探讨其对合作困境等问题的影响，发现相关因素对合作者或惩罚者丰度的作用，理论结果经模拟验证。
AI 中文摘要
公共物品博弈是研究冲突情境中合作出现与维持的重要范式。传统公共物品博弈中，表征共同努力协同效应的倍增因子通常假定为常数。但现实中投资回报常是动态的，随互动群体的策略构成而变。本文引入依赖于博弈群体内策略构成的一般频率依赖倍增因子，通过理论分析得出合作占优的数学条件。结果表明合作相对于背叛是否具有进化优势取决于博弈群体完全贡献状态下的投资回报率。还将该因子引入有同伴惩罚的公共物品博弈，系统探讨其对合作困境和二阶搭便车问题的影响。结果显示合作者或惩罚者的丰度仅由群体完全合作和完全惩罚构成下的投资回报值决定。完全合作状态下更高的回报率促进合作，完全惩罚状态下更高的回报率有利于惩罚行为出现。理论发现通过基于个体的模拟得到验证。
英文摘要
The public goods game serves as a significant paradigm for investigating the emergence and maintenance of cooperation in conflicting situations. In the traditional public goods game, the multiplication factor characterizing the synergy effect of common efforts is typically assumed to be constant. In real-world scenarios, however, investment returns are often dynamic and vary with the strategic composition of the interaction group. To date, the evolutionary dynamics of the public goods game with such frequency-dependent returns have remained not fully understood. In this work, we introduce a general frequency-dependent multiplication factor that depends on the strategy composition within the game group. Through theoretical analysis, we derive the mathematical conditions under which cooperation is favored. Our results show that whether cooperation has an evolutionary advantage over defection depends on the investment return rate in the full-contribution state of the game group, irrespective of the return rates in other states. An increase in this rate leads to a higher abundance of cooperators. Furthermore, we introduce a general frequency-dependent multiplication factor into the public goods game with peer punishment, and systematically explore its effects on the cooperation dilemma and the second-order free-rider problem. Our results highlight that the abundance of cooperators or punishers is governed solely by the investment return values in the full-cooperation and full-punishment compositions of the group. A higher return rate in the full-cooperation state facilitates the promotion of cooperation, whereas a higher return rate in the full-punishment state favors the emergence of punishment. Our theoretical findings are verified by individual-based simulations.
DOI：10.1016/j.physd.2026.135303
