## 3 Cache Strategy Formulation Based on Stackelberg Game  
This section considers the interests of multiple parties, such as mobile content providers and UAVs, in cache services. We model the pricing of content providers and caching strategies for UAVs as a Stackelberg game, with content providers acting as leaders and setting prices for files based on their own profit considerations. UAVs act as followers, making caching decisions based on the file prices set by content providers and predicting user request patterns, aiming to maximize their own utility objectives. As the leader in the Stackelberg game model, the content provider optimizes the file rent within a certain range of values to maximize its own benefits, and the content provider file rent pricing optimization problem is expressed as:  
\[ \begin{split}\text{P2}:\max&\;U_{cp_{x}}=\sum\limits _{f\in\mathcal{F}}c_{x,f}v_{x,f}\\ \text{s.t.}&\;v_{x,f}\in[v_{x,f}^{0},v_{\kappa,f}^{ initial}]\\ \end{split}  \tag{15}\]  
where the optimization objective is to maximize the revenue of the content provider, \(c_{x,f}\) is the caching decision variable of the UAV, \(v_{\kappa,f}\) denotes the file pricing of the operator, and \(v_{\kappa,f}\in[v_{\kappa,f}^{0},v_{\kappa,f}^{initial}]\). \(v_{\kappa,f}^{initial}\) represents the initial pricing for the file \(f\) and \(v_{\kappa,f}^{0}\) represents the minimum pricing. In the Stackelberg game model, the UAV, as a follower, makes its own caching decisions based on the file price given  
The optimization problem for the follower is initially considered. The premise of the algorithm is based on the assumption that the rental prices of files are given. The algorithm employs a greedy approach, whereby the UAV is inclined to cache files that are currently promising higher returns. This enables the UAV to tackle the optimization problem of determining the optimal caching decision. User requests are forecasted using the Zipf distribution. The probability of user \(n\) on channel \(m\) requesting file \(f\) is denoted \(q_{m,n,f}\). The revenue from caching a single file by the UAV can be represented as \(U_{f}=(\sum\limits_{m=1}^{M}\sum\limits_{n=1}^{N_{M}}q_{m,n,f}v_{cache}-\min \{v_{1,f},v_{2,f}\})\). The specific UAV caching placement strategy can be expressed as follows. When \(U_{f}>0\) and the remaining cache capacity \((S-\sum\limits_{f\in\mathcal{F}}c_{\kappa,f}Q)>0\), the UAV will purchase and cache the file from the content provider offering the lower rent. If both providers offer the same rent, the UAV will choose from which provider to purchase based on a certain probability. For solving the optimization problem of leaders, due to the fundamental similarity in file content across the libraries of various content providers and the direct price competition between the two content providers, the Bertrand game is introduced for modeling purposes. The Bertrand game model represents a form of price competition model where two or more enterprises compete by setting appropriate prices to sell identical products. In this paper, content providers are conceptualized as two enterprises engaged in a competitive Bertrand game, with each content provider pursuing the maximization of its own profit independently by determining its own file prices. It is assumed that under the condition where prices do not exceed the valuation of files by the UAV, the UAV will purchase and cache a single file from the content provider with the lower price. Consequently, content providers need to continually adjust file prices to achieve the maximization of their profits, considering factors such as costs, market demand, and competitors' pricing strategies. Under the current file pricing scenario, if the profits of the two content providers are equivalent, then the game reaches equilibrium, implying that no content provider can unilaterally adjust prices to attain higher profits. In this paper, as leaders, the content providers initially provide their initial rental price \(v_{\kappa,f}^{initial}\) for each file.