College of Science, Northwest A&F University, Yangling 712100, People's Republic of China.
College of Economics and Management, Northwest A&F University, Yangling 712100, People's Republic of China.
Proc Biol Sci. 2024 Jun;291(2024):20240182. doi: 10.1098/rspb.2024.0182. Epub 2024 Jun 12.
In contemporary society, the effective utilization of public resources remains a subject of significant concern. A common issue arises from defectors seeking to obtain an excessive share of these resources for personal gain, potentially leading to resource depletion. To mitigate this tragedy and ensure sustainable development of resources, implementing mechanisms to either reward those who adhere to distribution rules or penalize those who do not, appears advantageous. We introduce two models: a tax-reward model and a tax-punishment model, to address this issue. Our analysis reveals that in the tax-reward model, the evolutionary trajectory of the system is influenced not only by the tax revenue collected but also by the natural growth rate of the resources. Conversely, the tax-punishment model exhibits distinct characteristics when compared with the tax-reward model, notably the potential for bistability. In such scenarios, the selection of initial conditions is critical, as it can determine the system's path. Furthermore, our study identifies instances where the system lacks stable points, exemplified by a limit cycle phenomenon, underscoring the complexity and dynamism inherent in managing public resources using these models.
在当代社会，有效利用公共资源仍然是一个备受关注的问题。一个常见的问题是，叛逃者试图为个人利益获取过多的资源份额，这可能导致资源枯竭。为了减轻这种悲剧并确保资源的可持续发展，实施奖励遵守分配规则者或惩罚不遵守者的机制似乎是有利的。我们引入了两种模型：税收奖励模型和税收惩罚模型来解决这个问题。我们的分析表明，在税收奖励模型中，系统的进化轨迹不仅受到税收的影响，还受到资源自然增长率的影响。相比之下，税收惩罚模型与税收奖励模型具有明显不同的特征，特别是存在双稳性的可能性。在这种情况下，初始条件的选择至关重要，因为它可以决定系统的路径。此外，我们的研究还确定了系统缺乏稳定点的情况，例如极限环现象，这突出了使用这些模型管理公共资源的复杂性和动态性。
