Stochastic differential game model of diversified supply of emergency medical supplies led by government

The outbreak of COVID-19 has highlighted the importance of emergency medical supplies in responding to major public health emergencies. However, the supply of emergency medical supplies is highly random due to the impact of uncertain factors such as production cycle, raw material supply, virus mutation, and control measures. Based on the background of internal and external random factors of the epidemic, this paper studies the practical problems of a government-led continuous supply of diversified materials to build a stochastic differential game model for government-enterprise coordinated prevention and control of public emergencies and describes different prevention and control strategies of the government and enterprises with decentralized decision-making of anarchic cost subsidies, decentralized decision-making with government subsidies and centralized decision-making. The conditions of cooperation between government and enterprise were discussed. The influence of random factors in the model was identified by the expected value and variance of the supply of epidemic prevention materials. The optimal trajectory of the equilibrium strategy, the supply of epidemic prevention materials, and the system equilibrium income over time were obtained. The results show that if and only if the income distribution coefficient is within a certain threshold range, the centralized cooperation between government and enterprise achieves Pareto optimization. Government subsidies are effective in guiding enterprises, improving the prevention and control efforts of enterprises and the benefits of both parties, and alleviating the double marginal effect of non-government subsidy decisions. Under centralized decision-making, the expected value and variance of the supply of epidemic prevention supplies are the highest, that is, higher returns require greater risks. When the intensity of random interference increases, the fluctuation range of system returns will be more severe. Therefore, for subjects with different risk preferences, different cooperation modes will be produced, that is, enterprises with risk preference choose cooperation mode, while enterprises with risk aversion prefer the other two dispersion modes. © 2023 Systems Engineering Society of China. All rights reserved.