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.

在本文中，我们构建了第一个随机广义纳什均衡模型，用于研究国家之间在 Covid-19 大流行的备灾和响应阶段对有限医疗用品（PPE、呼吸机等）供应的竞争。每个国家的政府都面临着一个两阶段的随机优化问题，第一阶段是在宣布大流行之前，第二阶段是在宣布大流行之后。我们提供了理论结构、定性分析和算法，并附有收敛结果。受 N95 口罩和呼吸机需求的启发，提供了两个说明性示例以及算法求解的数值示例。结果表明，除了各国在宣布大流行之前做好准备外，他们在不同情况下适应条件的能力对其在大流行危机管理中的总体成功产生了重大影响。该框架可以捕捉对其他医疗用品的竞争，包括 Covid-19 疫苗和可能的治疗方法，并进行修改以处理易腐性。