# Collaborative Allocation Method of En-Route Network Resources Based on Stackelberg Game Model
## 2 Analysis of the Game Process in Collaborative Allocation of En-Route Network Resources  
### Game Construction and Principle Analysis  
Collaborative allocation of en-route network resources involves both ATC, which makes overall decisions, and participating airlines, which have an impact on the decision-making process. In this game process, ATC, as the ultimate decision-maker, has the right to take priority action and determine the final allocation plan and acts as the leader in the game process, while airlines, as participants, need to choose the plan according to the initial decisions made by ATC, playing the role of followers. This constitutes a Stackelberg game. The Stackelberg game is a staged decision problem involving a leader and one or more followers, in which the leader announces their strategy, and the followers make their own decisions or improvements based on the leader's strategy. The main idea of the Stackelberg game is that both the leader and the followers make decisions based on the possible strategies the other party may adopt to maximize their own interests or minimize their losses, aiming to achieve a stable state. The game process of collaborative allocation of en-route network resources mainly involves the following principles:  
1. Principle of individual rationality: In this game process, both ATC and the airlines, as individual entities participating in the game, are absolutely rational. ATC pursues the overall system optimum, including efficiency and fairness. Efficiency refers to the overall optimality of the system, encompassing both the entire air traffic management system and the objectives pursued by individual airlines during the game process. Fairness refers to the equitable treatment of all participating parties during the game process. It can also be understood as ensuring that there is no undue favoritism towards any specific airline throughout the gaming process. The initial allocation plan has already taken this condition into account, so this constraint does not need to be considered in the subsequent game. Each airline aims to maximize its own interests, specifically minimizing the total delay time of all flights belonging to the airline. (For airlines, there are numerous factors influencing total costs. However, for the purpose of simplifying calculations and ensuring a more intuitive presentation of results, we assume that maximizing the airline's interests is equivalent to minimizing the total delay time). There are no alliances between airlines, and the final allocation plan obtained through the game process should result in less delay time than the random selection, so that airlines will actively participate in the collaborative decision-making process. 2. Principle of relatively optimal strategy: In the case that no matter which plan other airlines choose, the plan chosen by the airline can ensure that its delay time is no less than other plans, then this plan is called the optimal strategy of the airline. In the game process, each airline pursues its own optimal strategy. When all airlines implement the optimal strategy, the system also reaches an optimal state. However, in the actual game process, due to the conflicts of interest, it is impossible to achieve the optimal state of each airline. Therefore, the final equilibrium is determined by ATC to achieve a relatively optimal state for the entire system. To ensure the smooth progress of the game process and the effectiveness of the model, the following assumptions need to be made before establishing the model:1. There is no alliance among airlines, and the airlines have a purely competitive relationship. Each airline aims to minimize its own delay time and actively secure advantageous trajectories and time slots. This game is a non-cooperative game. 2. When airlines engage in the game, all airlines make strategy selection among the feasible plans provided by ATC.