# Characteristic Analysis and Decision Model of Lane-Changing Game for Intelligent Connected Vehicles
## 4 Game Model
### Game Components
#### 4.2.1 Payoffs for Vehicle RV  
The efficiency gain of a vehicle should be defined as the increase or loss of time loss through the intersection. When the LV or RV decides to yield, it increases its own passing time and decreases its driving efficiency, and, conversely, when the RV makes the decision not to give way, it decreases its own passing time. The efficiency gains of the RV include travel gains and space gains. When the RV position is ahead of the LV, the RV not only narrows the travel time, but also has the initiative in space relative to the LV, and the same for the LV as well. The driving space gain of the vehicle is expressed as:  
\[P_{\rm s}=\frac{L_{space}}{L_{s,max}-L_{s,min}} \tag{2}\]  
where \(L_{space}\) indicates the spatial extent obtained with the current state of the vehicle and \(L_{s,max}\) and \(L_{s,min}\) are the maximum and minimum spatial ranges obtained based on the statistical results of the data. Figure 2: The diagram of the right of way. The efficiency gain of the RV not giving way is expressed as:  
\[P_{eff}^{RV}=P_{s}\cdot\frac{t_{curr}^{RV}-t_{min}^{RV}}{t_{max}^{RV}-t_{min}^{RV}} \tag{3}\]  
where \(t_{curr}^{RV}\) is the time to cross the intersection from the current position corresponding to the different decisions made by the RV; \(t_{max}^{RV}\) is the maximum time for the RV to pass the intersection considering the game with the LV; and \(t_{min}^{RV}\) is the time for the vehicle to cross the intersection at a steady speed. The safety gain of the vehicle is generally measured by the relative distance of the vehicle. Widely used in lane-change research is the minimum safe distance model, which takes into account the dynamic change process of vehicle lane changes when the vehicle meets the requirements of Equation (4), such that the vehicle can be safely changed. \[S_{t}=\int_{0}^{t}\left(\int_{0}^{s}\left(a_{L}(\tau)-a_{R}(\tau)\right)d\tau d \zeta\right)+\Delta v_{0}\cdot t+S_{0}\geq S_{min} \tag{4}\]  
where \(a_{L}\) and \(a_{R}\) are the accelerations of the LV and RV, respectively; \(\Delta v_{0}\) is the initial speed difference of the vehicles; and \(S_{0}\) is the initial workshop distance. \(S_{t}\) should be greater than the minimum vehicle distance \(S_{min}\). Since the safety of vehicles interacts with each other, the lane-changing game requires both sides of the game to make corresponding decisions; when the LV changes lanes, it requires the RV to slow down to provide lane-change spacing for the LV. Equation (5) shows the safety gain of the vehicles. \[P_{safe}^{RV}=\frac{S_{vch}-S_{min}^{vch}}{S_{max}^{vch}-S_{min}^{vch}} \tag{5}\]  
where \(S_{vch}\) is the longitudinal vehicle distance; \(S_{max}^{vch}\) is the maximum gaming distance (when the workshop distance is greater than the maximum gaming distance, the LV can change lanes without gaming); and \(S_{min}^{vch}\) is the minimum shop distance for the rear vehicle to take the maximum deceleration to provide the lane-change spacing for the LV. Considering the prospect of the development of ICVs, we built a game matrix by considering passenger expectations. The ICVs control the vehicle driving through the autonomous decision-making system, and the identity of the driver changes from the driver to the vehicle passenger. The ICVs should meet the passenger expectations under different driving scenarios, under the condition of complying with traffic rules; for example, the vehicle should not be too conservative and increase the travel time, and should not be too aggressive and reduce comfort. In this paper, we consider passengers' expectation requirements for vehicle decisions in the game payoffs by dynamically adjusting the vehicle's weight in terms of efficiency and safety. The game gain of the RV is mainly affected by the LV changing lanes; when the LV changes lanes and drives in front of the RV, it increases the waiting time of the RV through the intersection and decreases the efficiency gain; if the RV does not give way, it will increase the risk of decision conflict and decrease the safety gain.