Automated steering technology offers significant benefits to the safety of vehicles, but desire to keep the human driver in the loop requires a better understanding of the interaction between driver and vehicle. An existing noncooperative-game-theoretic framework for modelling such interaction is revisited, leading to the development of two driver steering control models. Both bear Nash-equilibrium properties, but involve different assumptions about driver steering behaviour. A simulation study is performed to demonstrate the difference between the two driver models. An experiment using a fixed-base driving simulator is conducted to measure six test subjects' steering angles in response to the lane-change manoeuvres generated by an automated steering controller. The two driver models' capabilities for representing driver steering behaviour are investigated through fitting them to measured driver steering angles. Key model parameters are identified using a system identification procedure. It is found that the two driver models have equivalent capability in capturing the trend of the six test subjects' measured steering angles, but less good at reproducing the overshoot and oscillation involved in two subjects' steering angles. It is found that the inclusion of an arm neuromuscular system model can improve the performance of the proposed driver models.