## 2 Methods and Model
### Model  
#### 2.2.1 Modeling Approach  
Firstly, it is important to clarify the specific problem and application scenario for spectrum allocation. The multi-agent, mixed-game decision-making for spectrum allocation is based on game theory methods, using MCM algorithm as the strategy for spectrum allocation, and employing the CRF algorithm as evaluation metrics for agent rewards and punishments to adjust frequency selection strategies. To accelerate the computational speed of the algorithm, perturbation methods are used to enhance the Monte Carlo acceleration algorithm. The multi-agent spectrum allocation approach based on MCCFR is illustrated in Figure 1.  
(1) Environment Modeling  
Game Environment: construct a game environment capable of simulating tasks such as electromagnetic spectrum management, including parameters such as spectrum characteristics, equipment deployment locations, action trajectories, timing of actions, and frequency usage priorities. State Representation: define the state for each agent, including its position, spectrum usage, and opponent behaviors. Reward Mechanism: design a reasonable reward mechanism to incentivize agents to take actions that align with the task objectives in a multi-agent game. (2) Agent Initialization  
Agent Types: define the different types of agents participating in the game, such as frequency management agents. Strategy Representation: represent each agent's strategy using an MCCFR network, which takes the current state as input and outputs the probability distribution of possible actions. (3) Strategy Update Based on CRF  
Counterfactual Regret Value Update: Before each game simulation, calculate the counterfactual regret values at each decision point and adjust strategies based on these regret values. For initial iterations, set the counterfactual regret values and frequency strategies at each decision point to 0.5, indicating equal probability for all frequency bands with no bias. (4) Sampling Strategy Based on MCM Algorithm  
Use Monte Carlo sampling methods to simulate multiple game processes, calculate regret values for each simulation, and obtain the average counterfactual regret values. Update strategies based on these values. (5) Game Model Training and Validation  
Conduct extensive simulations in the modeled environment to gradually update agent strategies. Determine the optimal strategies through rewards, punishments, and regret minimization. Establish reasonable validation metrics such as strategy payoffs, spectrum utilization, and action efficiency. Validate the model's performance in different task scenarios and analyze its feasibility and effectiveness in real-world applications. (6) Experimentation and Results Analysis  
Figure 1: Multi-agent, mixed-game decision-making for spectrum allocation approach. Set up various game task scenarios to simulate realistic electromagnetic spectrum management tasks. Evaluate the model's performance using experimental data and analyze its performance across different scenarios. Validate the effectiveness of each agent's strategy under different adversarial conditions, assess the performance and stability of various strategies, and ensure the achievement of intended goals in complex game environments. Based on experimental results, propose directions and methods for further optimizing the model. The red-blue confrontation is widely applied in various fields such as military, cybersecurity, and artificial intelligence training, serving as the foundation for multi-team confrontation research. In-depth study of two-party game problems not only lays a solid foundation for more complex multi-team confrontations but also provides an extensible decision-making framework. Therefore, this paper, based on the red-blue confrontation game scenario, utilizes the MCCFRA algorithm to achieve intelligent selection and decision-making, thereby enhancing the optimization capabilities of confrontation strategies. Next, we will briefly describe the process of building intelligent agents for both the red and blue parties