## 1 Introduction
### Related Work  
In the above method, the inherent adversarial dynamics between a legitimate UAV and a malicious jammer have led to the widespread adoption of game-theoretical methodologies to model their competitive interactions. Existing game-theoretical approaches can be broadly categorized into two types: non-cooperative and hierarchical models. Non-cooperative game models provide a mathematical lens to understand the simultaneous interactions between UAVs and jammers, anchored on the principle of Nash equilibrium solutions [12; 13; 14; 15; 16; 17; 18; 19; 20]. For instance, ref. [12] introduces a bimatrix game that sets out the conditions for a Nash equilibrium strategy within linear constraints. The study in [14] delves into channel coding in the face of adversarial jammers, revealing a convergence of game-theoretical and information-theoretical approaches in UAV communications over time. Meanwhile, the security challenges in cognitive radio networks, especially jamming attacks, are explored in [16], proposing game-theory-modeled anti-jamming strategies that utilize channel hopping and randomized power allocation. A passive anti-Primary User Emulation (PUE) approach, reminiscent of random frequency hopping, is discussed in [18]. Further, to address bandwidth and hardware limitations of FHSS signals, a channelized modulated wideband converter (MWC) scheme is proposed in [19]. Lastly, ref. [20] focuses on the distributed channel selection cooperative anti-jamming problem in UAV communication networks, suggesting an interference sensing cooperative anti-jamming scheme based on the Markov game framework. However, the non-cooperative game model presents challenges, including coordination issues, limitations in cluster networking adaptability, and difficulties in achieving convergence in expansive network settings. In the intricate dance of spectrum jamming, the decision-making interplay between a transmitter and a jammer often adheres to a hierarchical sequence. This can be aptly represented through a Stackelberg game model. In this setup, the transmitter, assuming the role of the leader, orchestrates an optimal strategy, fully cognizant of the jammer's impending best response. A plethora of studies have ventured into crafting Stackelberg game solutions tailored for jamming attacks in wireless communications [21; 22; 23; 24; 25; 26; 27; 28; 29; 30]. For instance, ref. [22] delves into power control dynamics, positioning the transmitter as the leader, empowered to select the optimal transmission power amidst a myriad of interference sources. Ref. [26] introduces an incentive mechanism, leveraging a coalitional game to galvanize legal UAVs into a coalition, with the Stackelberg game simulating the interplay between legal UAVs and adversaries. The findings underscore a marked enhancement in the anti-jamming prowess of UAV networks. Ref. [28] presents a game between a singular jammer and multiple users, pinpointing the Stackelberg equilibrium power dynamics. Moreover, ref. [29] harnesses a simulated annealing algorithm to discern the Stackelberg equilibrium, addressing power control intricacies within UAV communication networks' anti-interference framework. However, the Stackelberg game model grapples with challenges, such as reconciling the centralized leadership assumption with UAV networks' distributed essence and navigating uncertainties intrinsic to the Stackelberg paradigm. The integration of artificial intelligence (AI) algorithms to counteract jamming communication dilemmas has garnered substantial traction. Jammers, endowed with learning capabilities, can fluidly recalibrate their jamming tactics, adeptly sensing the spectral milieu. This agility renders traditional anti-jamming mechanisms somewhat obsolete, catalyzing a shift towards AI-centric solutions [31; 32; 33; 34; 35]. For instance, ref. [32] reimagines power allocation challenges in adversarial contexts, crafting algorithms that approximate the Nash equilibrium between communicators and a jammer. Ref.