<p>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. To overcome this challenge, 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. Further, an interaction disturbance function is used to quantify the impact of indirect interactions on ego vehicle. Then simulations with single and multiple conflict areas settings in a four-armed intersection are carried out. Simulations and human-in-the-loop simulator experiments show that the proposed algorithm can improve the interaction safety in intensively interactive driving scenarios even in complex and urgent interaction cases. The proposed framework may be potentially applied in handling autonomous vehicle's dynamic interactions with multiple road users.</p>