For autonomous driving, it is important to develop safe and efficient decision algorithms to handle multi-vehicle interactions. Game theory is suitable to manage the interactive driving decision modelling, however, common approaches of multi-player game formulation is computationally complex for dynamic and intense interactions.  The main contributions of this work are two-fold: 1) a global sorting-local gaming framework, namely GLOSO-LOGA, is proposed to solve the intersection interaction problem for autonomous driving, which can comprehensively consider the advantages of multi-vehicle collaboration and single-vehicle intelligence approaches; 2) an interaction disturbance function is used to quantify the impact of indirect interactions on ego vehicle. To validate the algorithm performances, corner case simulations and human-in-the-loop simulator experiments are carried out, in which a four-armed intersection scenario with various urgent and challenging interaction conditions is used. Results show that compared to the traditional approach that decomposes a multi-vehicle game into multiple two-vehicle games, the proposed algorithm can improve both safety and traffic efficiency in intensively interactive driving scenarios even in complex and urgent cases. It may be potentially applied in handling autonomous vehicle’s dynamic interactions with multiple road users.