# Game Theory-Based Interactive Control for Human-Machine Cooperative Driving
## 1 Introduction  
Benefiting from the advancement of science and technology, such as computer science, communication networks, and smart chips, autonomous driving technology has progressed rapidly in recent years. The Society of Automotive Engineers (SAE) used a six-level system (ranging from level 0 to level 5) in 2014 to define the degree of automation [1]. The current research on autonomous driving mainly focuses on the degree of level 3 [2], which allows for switching between fully autonomous and fully manual driving modes. However, a variety of unresolved issues need to be addressed before fully autonomous driving can be achieved, including ethical issues, laws and regulations, and technical bottlenecks [2; 3; 4; 5]. In addition, keeping the driver out of the control loop for a long time will lead to driver over-reliance and situational awareness decline [4; 6]. However, it is worth noting that automation control systems surpass humans in information storage, computing power, etc., while human drivers exceed automation in moral judgment and reasoning [2]. Shared control technology in intelligent driving can make full use of the strengths of human drivers and automation systems to compensate for each other's weaknesses, which has been considered a transition to fully autonomous driving [7]. The concept of shared control was first proposed by [PERSON] and [PERSON] in the field of industrial robots in 1978 [8]. Subsequent research developed it towards intelligent vehicles and derived the idea of a human-machine shared control vehicle (HSCV) [2; 4; 6]. The standard shared control system in an HSCV consists of a human driver, an automation control system, a control mechanism, and a controlled vehicle system [6]. The driver in a shared control system sits in the driving seat and controls the future movement of the vehicle by turning the steering wheel and adjusting the accelerator and brake pedals. The unique aspect of shared control in an HSCV is that the driver and the automation control system are simultaneously kept in the control loop to complete a specific driving task together [2]. The control mechanism is used to integrate the driver's control commands and the control actions of the automation system and ultimately input them into the vehicle system. Based on the different control mechanisms, the shared control system in an HSCV can be divided into a haptic shared control system and an input mixing shared control system. The main difference between them is whether the control mechanism is mechanically coupled. Haptic shared control usually uses an electric power steering system to directly increase auxiliary torque to intervene and guide the driver's control commands [9]. In contrast to haptic shared control, a steer-by-wire system can be used by an input mixing shared control system to allow the steering wheel to be mechanically decoupled from the road wheel. It then uses an intermediate controller to modify control commands entered by the driver before they are applied to the vehicle steering system [2]. Designing a proper control policy for the automation system is always one of the critical issues in the shared control system. An appropriate control policy is expected to consider drivers' personalization and commands to minimize human-machine conflicts and guarantee driving safety and stability in changeable traffic scenarios [4; 6]. For shared control, integrating driver modeling into the system to characterize driver behavior can increase mutual understanding between the driver and the automation system, thereby reducing human-machine conflicts [2; 10]. Many studies based on driver models have been conducted, including the single-point preview model [2] and the two-point preview model [11; 12], which are used to simulate the driver's steering behavior in lane keeping scenarios and obstacle avoidance scenarios. [PERSON] et al. [13] adopted the idea in the work [14] that driver steering behavior can be simulated by model predictive control (MPC), and they designed a driver steering model based on MPC.