Human–machine shared control of intelligent vehicles is considered an important technology during the industrial application of autonomous driving systems. Among the engineering practices in driver assistance systems, shared steering control is one of the important applications for the human–machine interaction. However, how to deal with human–machine conflicts during emergency scenarios is the main challenge for the controller’s design. Most shared control approaches usually generate machine-oriented results without enough attention to the driver’s reaction. By taking the human driver and machine system as two intelligent agents, this paper proposes a game-based control scheme to achieve a dynamic authority allocation during the lane changing maneuver. Based on the modeling of predicted trajectories of the human driver, a human-intention-based shared steering control is designed to achieve dynamic Nash game equilibrium. Moreover, a human-oriented shared steering mechanism is employed to not only benefit from automated machine assistance, but also make full play of human contributions. Using quantitative comparative analysis in lane changing scenarios with different human–machine conflicts, a better performance by considering both driving comfort and safety is achieved.