## 1 Introduction
When applied to the multi-agent domain, this leads to multi-agent deep reinforcement learning, which is currently one of the most promising directions [15]. The introduction of game theory provides a theoretical foundation for handling competitive and cooperative relationships among multiple agents, while also defining optimal strategies through Nash equilibrium in stochastic games [16]. The MaxMinQ-learning algorithm addresses the zero-sum game problem for two players [17]. The Nash-Q-learning algorithm uses quadratic programming to solve Nash equilibrium points, tackling general multi-agent games [18]. The WoLF-PH algorithm, by employing the PHC algorithm to learn and improve strategies, replaces the quadratic programming approach and reduces the algorithmic complexity, significantly enhancing convergence speed [18]. [PERSON] and colleagues introduced evolutionary algorithms into multi-agent systems, enabling agents to exhibit collaborative evolution. However, this approach applies only to agents operating under cooperative relationships [19; 20; 21]. The introduction of deep learning has provided novel approaches for multi-agent reinforcement learning. The Multi-Agent Deep Deterministic Policy Gradient(MADDPG) algorithm improves upon traditional Actor-Critic (AC) methods by employing a centralized training and decentralized execution approach. It enhances the experience replay mechanism and trains a Critic requiring global information and an Actor requiring local information for each agent. Additionally, each agent can have its own reward function. These improvements enable MADDPG [22] to handle both competitive and cooperative scenarios, as well as mixed game problems. However, due to the complex interrelations between agents in mixed games, this algorithm also faces challenges, such as the lack of a systematic basis for manually designing reward functions and difficulties in training multiple agents from scratch to converge. Therefore, research into reinforcement learning-based multi-agent cooperative adversarial methods holds significant value. [PERSON] et al. proposed an orthogonal genetic algorithm based on the idea of mixed niches. At the same time, we use a standard genetic algorithm and a micro genetic algorithm to optimize the model. The model has the advantages of fast convergence, strong stability and good optimization effect [23]. This method is only applicable to fixed scenario allocation and is not suitable for rapidly changing adversarial scenarios. [PERSON] et al. discuss some featured game models to investigate spectrum allocation for task-driven UAV communication networks [24]. However, the article did not apply it to practical scenarios and only discussed the application of game theory to spectrum allocation. In summary, multi-agent decision-making algorithms under mixed games have many areas that require improvement. Addressing the rules for the changing dynamics of a complex electromagnetic environment, this paper proposes a multi-agent hybrid game spectrum allocation method based on the Monte Carlo counter-factual regret minimization (MC-CFR) algorithm. The goal is to enhance the rationality, effectiveness, and intelligence of spectrum allocation in complex electromagnetic environment and to validate the feasibility and effectiveness of the MCCFR-based multi-agent hybrid game spectrum allocation module. The main contributions of this article are as follows: (1) It proposes a multi-agent hybrid game spectrum allocation method based on the MCCFR algorithm. This method addresses the dynamic changes in spectrum allocation within complex electromagnetic environments. Introducing a multi-agent hybrid game model based on the MCCFR algorithm enhances spectrum allocation's rationality, effectiveness, and intelligence.