Extensive manual driving is liable to attention lapses and driver exhaustion resulting in lane offset errors, driver comfort minimization and degradation in vehicle stability. On the contrary, apart from being expensive, autonomous vehicles suffer from the issue of trust, ethics and traffic mapping. In order to address the above limitations, this paper deals with the design of a Game Theoretic based Shared Control (GTSC) framework that enables an interaction between the human and the machine. The novelty lies in the generation of automatic driver automation relative weights based on the vehicle’s lateral position relative to the maximum admissible lateral offset. The interaction between the human driver and automated system based on the cooperative game theory is utilized to develop a robust shared control framework. The driver model parameters have been estimated using the experimentally obtained driver steering torque and steering wheel angle respectively through an inverse modelling procedure. The lateral dynamics of the vehicle model in the presence of crosswinds and yaw moment as disturbances are considered for the design. A higher order sliding mode observer is designed to ensure robust estimation of the unknown states. Unlike the existing studies that primarily concentrates on the robust game theoretic shared controller design, this new study broadens its focus. The study introduces an observer-based robust design for GTSC and establishes the stability of the closed-loop system. The effectiveness of this proposed framework is verified through simulations in Carsim as well as real-world testing on a Hardware-in-the-loop (HIL) platform with a human driver. The study also addresses the challenge of obstacle avoidance using the GTSC framework. Comparisons have been performed with the state-of-the-art shared control studies while considering factors like crosswinds, variation in the longitudinal velocities and alterations in the reference path to evaluate the effectiveness of the proposed shared control study. The results demonstrate the improvement in the lateral offset, driver comfort and the vehicle stability compared to the manual control of the vehicle.