# Biform Game Approach to Strategy Optimization of Autonomous Vehicle Lane Changes on Highway Ramps
## 4 Example Analysis
### Numerical Analysis  
#### 4.4.1 Parametric Analysis  
Using the above biform game method for the speed distribution of the target lane's leading vehicle, the lane-changing vehicle, and the following vehicle, we conducted the following analysis: When the acceleration probability of the leading vehicle and the deceleration probability of the following vehicle are determined, the forced lane-changing probability of the lane-changing vehicle results were adjusted as a linear increase in the optimal stable speed of the three vehicles with respect to the forced lane-changing probability. Moreover, the rate of speed change of the target lane-changing vehicle was greater than that of the leading and following vehicles, as shown in Figure 2a. When the forced lane-changing probability of the target vehicle and the acceleration probability of the leading vehicle were determined, adjusting the deceleration probability of the following vehicle did not affect the optimal stable speed of the three vehicles, as shown in Figure 2b. This is related to the real optimal goal of the three vehicles passing through the intersection as quickly as possible. To achieve the fastest passage while allowing the following vehicle to yield to the lane-changing vehicle, a constant speed rather than a deceleration driving strategy was adopted. When the forced lane-changing probability of the target vehicle and the deceleration probability of the following vehicle were determined, adjusting the acceleration probability of the leading vehicle resulted in a linear increase in the optimal stable speed of the three vehicles with respect to the acceleration probability of the leading vehicle, and the rate of speed change of the leading vehicle was greater than that of the target lane-changing vehicle and the following vehicle, as shown in Figure 2c. By analyzing the influence of the acceleration probability of the lead vehicle, the deceleration probability of the following vehicle and the forced lane-change probability of the target lane-changing vehicle at the optimal stable speed (with the forced lane-change probabilities of the target vehicle fixed at \(\mu_{i}\) 0.25, 0.50, 0.75, and 1.00) and the values of the lead vehicle's acceleration probability and the following vehicle's deceleration probability, as shown in Figure 3a-d, it can be observed that the optimal stable speed of the three vehicles exhibited a linear increase with an increase in the acceleration probability of the lead vehicle and the optimal stable speed also increases with the rise in the forced lane-change probability of the target vehicle. From Figures 2 and 3, it can be seen that the optimal stable speed of the three vehicles was independent of the deceleration probability of the following vehicle. Therefore, by fixing the deceleration probability of the following vehicle, we analyzed the impact of the acceleration probability of the leading vehicle and the forced lane-changing probability of the target vehicle on the optimal stable speed. As shown in Figure 4, the optimal stable speed exhibited a linear increasing relationship with both the acceleration probability of the leading vehicle and the forced lane change probability of the target vehicle. This is consistent with the conclusions drawn from analyzing Figure 2, and it can be observed that the impact of the forced lane change probability on the optimal stable speed was greater than that of the leading vehicle's acceleration probability. The results presented in Figures 2-4 are the specific manifestations of the biform game model under different parameters. They are closely related to the model and reflect and verify the characteristics and value of the model from multiple aspects. 1. Model optimization results: The biform game model aims to maximize the interests of lane-changing vehicles and affected vehicles, enabling vehicles to adjust to the optimal equilibrium speed.