论文标题
当自私投资者利用可退化的公共资源时，通用的灾难性贫困
Generic catastrophic poverty when selfish investors exploit a degradable common resource
论文作者
论文摘要
当许多自私的投资者过分利用时，普通资源池的生产率可能会降低，这种情况被称为公共场所（TOC）。没有法规，代理人通过平衡产生的成本与收到的收益来优化其个人投资的规模。由此产生的NASH均衡涉及个人投资决策与公地状态之间的自洽循环。结果，出现了几种非平凡的特性。对于$ n $投资参与者，我们严格地证明，典型的收益不缩放为$ 1/n $，这是合作代理商的预期结果，而是$（1/n）^2 $。因此，关于$ n $的功能依赖的收益降低了，这种情况表示灾难性贫困。我们表明，灾难性的贫困是由于回报和成本之间的微调平衡而产生的。此外，可能存在有限数量的寡头。寡头的特征是有限的收益，当$ n $增加时不会减少。我们的结果适用于通用类别的模型，包括凸面和中等凹入的成本功能。为了强烈的凹入成本，纳什均衡经历了集体重组，其特征是进入障碍和突然的死亡强迫市场退出。
The productivity of a common pool of resources may degrade when overly exploited by a number of selfish investors, a situation known as the tragedy of the commons (TOC). Without regulations, agents optimize the size of their individual investments into the commons by balancing incurring costs with the returns received. The resulting Nash equilibrium involves a self-consistency loop between individual investment decisions and the state of the commons. As a consequence, several non-trivial properties emerge. For $N$ investing actors we prove rigorously that typical payoffs do not scale as $1/N$, the expected result for cooperating agents, but as $(1/N)^2$. Payoffs are hence reduced with regard to the functional dependence on $N$, a situation denoted catastrophic poverty. We show that catastrophic poverty results from a fine-tuned balance between returns and costs. Additionally, a finite number of oligarchs may be present. Oligarchs are characterized by payoffs that are finite and not decreasing when $N$ increases. Our results hold for generic classes of models, including convex and moderately concave cost functions. For strongly concave cost functions the Nash equilibrium undergoes a collective reorganization, being characterized instead by entry barriers and sudden death forced market exits.
