食品质量管理问题驱动的非线性微分博弈研究：均衡分析与保序性态

食品质量与民生息息相关，其重要性不言而喻。面对消费者日益增强的食品质量需求，零售企业能否随时间动态调节质量竞争策略对于其利润增长，甚至成败都至关重要。微分博弈，作为连续时间下的决策工具，虽在工业耐用品的质量管理中已有应用，但在用于生鲜食品的质量管理时，却遭遇理论瓶颈。其深层原因在于生鲜食品的质量衰退方程中含有非线性项，由此导致相应的微分博弈模型无法获得解析解，进而不能按传统方式进行敏感性分析和政策探讨。受此驱动，本项目拟针对一般形式的非线性微分博弈问题，利用微分变分不等式和不动点理论，探索其开环Nash均衡解的存在性、唯一性及保序性态。然后，将获得的新理论应用于生鲜食品的质量管理中。本项目关于“保序性态”的理论研究不再依赖于解析解，因此可望为微分博弈的敏感性分析开辟一条全新的研究路径。此外，这种针对“一般形式的微分博弈”所进行的理论拓展，对于其它涉及非线性函数的经管问题也具有广阔应用前景。

Food quality is closely related to people's livelihood, and its importance is self-evident. In the face of the increasing demand of consumers for food quality, whether the retail enterprises can dynamically adjust the quality competition strategy over time is crucial for their profit growth, even for their success or failure. Differential game, as a decision-making tool used for continuous time, has been used in the quality management of industrial durable goods, but it encounters theoretical bottleneck when it is used in the quality management of fresh food. The primary reason lies in the existence of the non-linear term in the quality decline equation of fresh food. Consequently, it is hard to obtain the analytical solution for the corresponding differential game model, and thus it is unable to carry out the sensitivity analysis and policy discussion in the traditional way. Driven by this, the present project aims to explore the existence and uniqueness of the open-loop Nash equilibrium solution and the order-preserving behaviors of the nonlinear differential game problem in the general form by using the differential variational inequality and fixed point theory. Then, the new obtained theory would be applied to the quality management of fresh food. The theoretical study on "order-preserving behaviors" in this project is no longer dependent on the analytical solutions, so it is expected to open up a new research path for sensitivity analysis of differential games. In addition, this kind of theoretical research on "the general form of differential games" has broad application prospects for other economics and management problems involving nonlinear functions.