## 1 Introduction  
Unmanned aerial vehicle (UAV) communication networks, as a kind of newly-developing wireless communication network, have become a hot research issue [1; 2]. When important tasks are carried out, how to construct a reliable and robust UAV network is of great significance. In some cases, the existence of a malicious jammer will have a great impact on communications among UAVs, which motivates us to investigate the anti-jamming approach in UAV communication networks. In the traditional anti-jamming research field, various techniques have been adopted, i.e., power control, uncoordinated frequency hopping (UFH) and frequency hopping spread spectrum (FHSS) [3]. However, there are some limitations using these techniques: (i) anti-jamming power control is ineffective under the circumstance of high jamming power; (ii) traditional UFH and FHSS consume a large amount of spectrum resources, and they are not able to work well under the dynamic spectrum environment [4; 5; 6]. As an example of the dynamic spectrum environment, the primary-secondary access scenario in cognitive radio networks has been investigated in [7]. In detail, the primary-secondary access scenario means the spectrum is owned by primary users and can be used by secondary users when it is idle. The spectrum holes, which can be accessed by secondary users, are time-varying, and the environment with spectrum holes is a kind of dynamic spectrum environment. Moreover, in [8], the authors investigated the distributed channel selection problem in an opportunistic spectrum access (OSA) system, in which the channel states are also time-varying. In [9], the authors studied the problem of distributed channel selection for interference mitigation in a time-varying environment, where the channels undergo block fading. This is also a kind of dynamic spectrum environment. In addition, game theory [9; 10; 11; 12], as a strong theoretical tool, is suitable to model the anti-jamming competitive scenario. Specifically, the Stackelberg game approach [12], as a kind of hierarchical game, has been widely used in the anti-jamming field. For example, in [13], the authors summarized the application of the Stackelberg game in anti-jamming dense networks and introduced several classical anti-jamming scenarios and system models. Moreover, an outlook on the application of the anti-jamming Stackelberg game was also made. In [14; 15; 16], the Stackelberg game approaches were adopted for the anti-jamming power control problem, where the user acted as the leader and the jammer acted as the follower of the game. Utility functions were designed, and Stackelberg equilibriums (SE) were also obtained via game approaches. Considering the channel selection problem under a malicious jamming environment, the authors proposed a hierarchical anti-jamming channel selection scheme using a Stackelberg game framework [17]. However, most existing studies under the Stackelberg game framework formulated the interactions between the user-side and jammer-side, which brought large deviation in information acquisition. In a word, studies focusing on anti-jamming channel selection under a dynamic jamming environment are of great importance. As an example of a dynamic jamming environment, in [14], the authors investigated the anti-jamming power strategies under the threat of a smart jammer. The jammer can adjust its jamming power adaptively according to the user's transmission power. As the jamming power strategies are not fixed, we can call it the \"dynamic jamming power environment\". Moreover, in [17], the authors investigated the anti-jamming channel selection problem, in which the channel selection strategies can be adjusted adaptively according to the users' channel strategies, and we can call it the \"dynamic jamming channel environment\". If the strategies of the jammer are not fixed, we view it as a kind of dynamic jamming environment. In fact, the dynamic feature of the channel state, which means the channel states are time-varying, brings some challenges to anti-jamming channel selection.