悲剧
公共物品游戏
公共物品
平民
复制因子方程
霍普夫分叉
进化博弈论
困境
激励
进化动力学
经济
博弈论
微观经济学
生态学
分叉
生物
社会学
数学
人口
物理
非线性系统
人口学
几何学
量子力学
作者
Chunpeng Du,Yikang Lu,Y.-C. Zhang,Chen Shen,Лей Ши,HW Guo
出处
期刊:Chaos
[American Institute of Physics]
日期:2024-04-01
卷期号:34 (4)
摘要
Feedback loops between strategies and the environment are commonly observed in socio-ecological, evolution-ecological, and psychology-economic systems. However, the impact of mutations in these feedback processes is often overlooked. This study proposes a novel model that integrates the public goods game with environmental feedback, considering the presence of mutations. In our model, the enhancement factor of the public goods game combines positive and negative incentives from the environment. By employing replicator-mutator (RM) equations, we provide an objective understanding of the system's evolutionary state, focusing on identifying conditions that foster cooperation and prevent the tragedy of the commons. Specifically, mutations play a crucial role in the RM dynamics, leading to the emergence of an oscillatory tragedy of the commons. By verifying the Hopf bifurcation condition, we establish the existence of a stable limit cycle, providing valuable insights into sustained oscillation strategies. Moreover, the feedback mechanism inherent in the public goods game model offers a fresh perspective on effectively addressing the classic dilemma of the tragedy of the commons.
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