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In recent years, rapid progress in autonomous driving has been achieved through advances in sensing, control, and learning. However, as the complexity of traffic scenarios increases, ensuring safe interaction among vehicles remains a formidable challenge. Recent works combining artificial potential fields (APF) with game-theoretic methods have shown promise in modeling vehicle interactions and avoiding collisions. Yet, these approaches often suffer from overly conservative decisions or fail to capture the nonlinear dynamics of real-world driving. To address these limitations, we propose a novel framework that integrates mean field game (MFG) theory with model predictive control (MPC) and quadratic programming (QP). Our approach leverages the aggregate behavior of surrounding vehicles to predict interactive effects and embeds these predictions into an MPC-QP scheme for real-time control. Simulation results in complex driving scenarios demonstrate that our method achieves multiple autonomous driving tasks while ensuring collision-free operation. Furthermore, the proposed framework outperforms popular game-based benchmarks in terms of achieving driving tasks and producing fewer collisions.