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Abstract：
In this paper, we construct the first stochastic Generalized Nash Equilibrium model for the study of competition among countries for limited supplies of medical items (PPEs, ventilators, etc.) in the disaster preparedness and response phases in the Covid-19 pandemic. The government of each country is faced with a two-stage stochastic optimization problem in which the first stage is prior to the pandemic declaration and the second stage is post the pandemic declaration. We provide the theoretical constructs, a qualitative analysis, and an algorithm, accompanied by convergence results. Both illustrative examples are presented as well as algorithmically solved numerical examples, inspired by the need for N95 masks and ventilators. The results reveal that, in addition to the preparedness of countries before the pandemic declaration, their ability to adapt to the conditions in different scenarios has a significant impact on their overall success in the management of the pandemic crisis. The framework can capture competition for other medical supplies, including Covid-19 vaccines and possible treatments, with modifications to handle perishability.
摘要：
在本文中,我们构建了第一个随机广义纳什均衡模型，用于研究国家之间对有限医疗物品供应的竞争(PPEs，呼吸机,等。)在新冠肺炎大流行的备灾和救灾阶段。每个国家的政府都面临着一个两阶段的随机优化问题，其中第一阶段是大流行宣布之前，第二阶段是大流行宣布之后。我们提供了理论结构，定性分析，和一个算法，伴随着趋同结果。给出了两个说明性示例以及算法求解的数值示例，灵感来自N95口罩和呼吸机的需要。结果表明,除了在大流行宣言之前各国的准备之外，他们适应不同情况的能力对他们在管理大流行危机方面的整体成功有重大影响。该框架可以抓住其他医疗用品的竞争，包括新冠肺炎疫苗和可能的治疗方法，修改以处理易腐烂性。
