# Spacing Allocation Method for Vehicular Platoon: A Cooperative Game Theory Approach
## 6 Conclusions  
The cooperative control method for vehicle platoon has been widely verified to improve the traffic capability and stability, and fuel economy. The overall performance of the platoon is mainly influenced by the spacing policy and motion controller. To ensure the string stability, traffic flow stability, and local stability, the spacing policy tends to be more complex in comparison with the CD policy and CTH policy. This paper proposes a systematic spacing policy for platoon based on the cooperative game theory.  
Figure 10: Longitudinal following error and stable time: (**a**) Initial velocity situation; (**b**) leading vehicle deceleration situation.  
To transform the platoon performance into the profit function of the desired spacing, we propose a spacing policy based on the bionic motion principles. A characteristic function is used to describe the cooperative game model of the platoon, hence it is possible to obtain the desired spacing through the distribution methods of profit, like Shapley value, \(\tau\) value, and \(AL\) value. Mathematical analysis proves that the proposed spacing policy with its motion controller can ensure string stability and traffic flow stability simultaneously compared with CD policy. To evaluate the effectiveness of the proposed method, simulation experiments are conducted, and the results can be concluded as follows:  
1. The initial errors with step input of the velocity error will be eliminated, and the platoon will form a new stable state with proposed method. The positions and velocities shown in the simulating results demonstrate that the vehicles can achieve consistency control for platoon in infinite time.
2. The platoon controlled with normal spacing policy, Shapley value and AL value can guarantee the local stability, string stability, and traffic flow stability. The results show that the errors will gradually converge and stop increasing upstream in platoon which agrees with the theoretical analysis.
3. Spacing is considered as the profit for distribution, and the platoon performance is related to the distribution methods based on the cooperative game theory. For example, \(AL\) value is an average distribution of the total profit on the basis of the minimum payoff which makes the vehicles drive in synchronization compared with other spacing policies.  
To expand the research, the characteristic function can be used to evaluate the different behavioral decisions and achieve Pareto optimality in complex scenarios, like cut-in, cut-out, and no signal crossing. For examples, it can be used to decide the travel order while two platoon conflict with each other in no signal crossing, and it will help to decide the optimal position for a new vehicle while join the platoon, etc. Besides, the available structure of the game model is relative to the information flow of the platoon which means that the directed graph game model can describe the vehicle's confliction when they can communicate with others limitedly. The cooperative game model and the mathematical analysis proposed in this paper will provide a foundation for these future extensions.  
Conceptualization, data curation, writing--original draft preparation, Y.L.; project administration, C.Z.; formal analysis, X.H.; methodology providing, D.Z.; Validation, H.Z.; data analysis, C.S.; All authors have read and agreed to the published version of the manuscript.  
This research was sponsored by Science and technology project of Jilin Provincial Education Department, No. JJKH20200963 KJ, and the National Natural Science Foundation of China under Grant (51575224).  
The authors declare no conflict of interest.