收获自我更新公共资源的生态进化博弈：收获者种群增长的影响
Eco-evolutionary games for harvesting self-renewing common resource: Effect of growing harvester population
摘要：
公地悲剧（英语：Tragedy of the Commons，TOC）是一个普遍存在的社会困境，在一群生物与共享资源之间的互动中被见证：群体中的个体倾向于自私地过度开发公共资源，因为这可以说是理性的选择，或者在非人类的情况下，这可能是进化上不可侵犯的行为。如何避免TOC是一个关系到节约资源的重大问题。不难设想这样的情况：资源可以自我更新，人口的规模可能取决于资源的状况，因为人口的不同部分采用不同的开采率。如果资源的自我更新率位于最大和最小开采率之间，那么在什么条件下可以避免TOC就不是先验的。在本文中，我们解决这个问题的分析和数值模拟使用的进化博弈理论复制子方程模型的达尔文主义的自然选择的宗旨设置。通过复制子方程，我们在研究复制子群体如何利用共享资源的同时，也不能忽略后者对前者的动态反馈。我们还提出了一个透明的自下而上的游戏资源反馈模型的推导，以方便未来的研究对本文提出的研究结果的随机效应。
英文摘要：
The tragedy of the commons (TOC) is a ubiquitous social dilemma witnessed in interactions between a population of living entities and shared resources available to them: The individuals in the population tend to selfishly overexploit a common resource as it is arguably the rational choice, or in case of non-human beings, it may be an evolutionarily uninvadable action. How to avert the TOC is a significant problem related to the conservation of resources. It is not hard to envisage situations where the resource could be self-renewing and the size of the population may be dependent on the state of the resource through the fractions of the population employing different exploitation rates. If the self-renewal rate of the resource lies between the maximum and the minimum exploitation rates, it is not a priori obvious under what conditions the TOC can be averted. In this paper, we address this question analytically and numerically using the setup of an evolutionary game theoretical replicator equation that models the Darwinian tenet of natural selection. Through the replicator equation, while we investigate how a population of replicators exploit the shared resource, the latter's dynamical feedback on the former is also not ignored. We also present a transparent bottom-up derivation of the game-resource feedback model to facilitate future studies on the stochastic effects on the findings presented herein.
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