## 2 Related Work
The authors [24] distinguish between pure, mixed, and stochastic Nash equilibrium. Through cooperative and competitive strategies, their work provides insights into how congestion and traffic distribution can be managed. In contrast with other game-theoretic models used in route planning, our model prioritizes emergency vehicles while maintaining overall network efficiency through Stackelberg games. Our approach incorporates hierarchical fairness mechanisms to ensure regular vehicles are not disproportionately affected by the prioritization of emergency traffic, as opposed to Nash equilibrium or pure Stackelberg games. Furthermore, we focus on real-time adaptive control rather than static route optimization. Congestion pricing is another area in which game theory has been applied. As a means of managing traffic across multiple regions in transportation networks, [25] propose cooperative and competitive congestion pricing schemes based on Stackelberg games. In these models, network efficiency is balanced with revenue generation. The Stackelberggame model was extended by [26], incorporating option theory to optimize intermodal freight pricing strategies [27]. Instead of focusing on congestion pricing or competitive pricing strategies, our work focuses on real-time control and fairness-based decision-making within a hierarchical traffic management system. We use a game-theoretic framework rather than price incentives to manage congestion, ensuring that emergency vehicles receive priority while all road users are kept fair. The combination of Nash and Stackelberg games has been explored in the planning of traffic routes and the control of traffic signals. Using Nash/Stackelberg Q-learning for traffic routes, [2] demonstrates how hybrid game models can optimize intersection traffic. In addition, [28] applied Nash game-based distributed control to balance traffic density across freeway networks, improving traffic-flow management significantly. Although existing studies have employed Nash and Stackelberg games for traffic control, our innovation lies in the hierarchical Stackelberg model, which introduces multiple levels of decision-making, namely the Traffic Management Center (TMC) as leader, emergency vehicles as first-level followers, and regular vehicles as second-level followers. Compared to conventional Stackelberg models, this hierarchical structure is more effective at handling emergency traffic scenarios. Fairness measures are also implemented, ensuring that regular traffic does not experience excessive delays despite emergency traffic being prioritized. To the best of our knowledge, this study is the first to investigate traffic congestion management using a hierarchical Stackelberg model. While numerous studies have explored traffic control using the standard Stackelberg framework, our contribution extends this by introducing a hierarchical structure, wherein decision-making occurs at multiple levels to better prioritize traffic. The results obtained from our model demonstrate its superiority over simpler Stackelberg approaches, showcasing improved efficiency and performance in managing both congestion and priority traffic scenarios.