Dynamic Stochastic Game Models for Collaborative Emergency Response in a Two-Tier Disaster Relief System

This study investigates collaborative disaster response strategies involving the government and social organizations from a dynamic perspective, incorporating stochastic disturbances that influence emergency resource supply. To examine the strategic interactions among the participants, three stochastic differential game models are formulated under distinct scenarios: centralized decision making for collusive emergency response, decentralized emergency response without a cost-sharing contract, and decentralized emergency response with a cost-sharing contract. Under an infinite-horizon planning framework, the closed-form solutions for the optimal response efforts and the corresponding value functions are derived for all three scenarios and comparatively analyzed. The results indicate that compared with the purely decentralized scenario, introducing a cost-sharing mechanism achieves a Pareto improvement by optimizing both overall system efficiency and emergency supply availability. Although the centralized collusive model results in the highest expected level of emergency resource supply, it is also associated with the greatest uncertainty. Furthermore, a numerical simulation based on emergency resource allocation during the Wenchuan earthquake is conducted. The results show significant differences in resource availability and response performance under different response mechanisms. Centralized collaboration, together with a well-designed cost-sharing mechanism, can significantly enhance the robustness and efficiency of the overall system, offering important insights for optimizing real-world disaster response strategies.