A new game theory based framework is proposed for path tracking and stabilization of autonomous vehicles. In the developed framework, vehicle body and corner traction control strategies are formulated in terms of players in a differential game. An integrated stability and path tracking control based on a non-cooperative differential game is developed. It includes bidirectional slip effect and wheel dynamics, which reflect more accurate longitudinal and lateral dynamics in harsh maneuvers and scenarios with sudden changes in the path planners trajectories. The open-loop and closed-loop Nash equilibrium control strategies are obtained by solving a two-player linear-quadratic differential game for the dynamical system of the overall tracking error. The performance of the proposed control strategy is validated with software simulations in various driving conditions.