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Offloading technique is an effective approach to migrate tasks from mobile devices to cloud to prolong the battery life. However, it cannot be guaranteed that all devices can successfully offload their tasks to cloud due to the limited network resources, thus offloading decisions should be made to coordinate devices. The existing works focus on how to maximize energy saving for a group of devices instead of the number of mobile devices that benefits from offloading. Therefore, how to maximize the number of energy-saving devices in the multi-user offloading scenario remains a challenging issue to be solved. In this paper, we aim to obtain a beneficial offloading group where all device can offloading tasks simultaneously to achieve energy saving and the number of beneficial offloading devices maximum for the group. In order to get such a group where each device can achieve its own benefit, firstly, we adopt game theory to model each device's demand of saving energy by offloading in OFDMA communication system, and formulate multi-user offloading game problem (MUOG). Furthermore, we propose an offloading game mechanism (OGM), including: beneficial offloading threshold (BOT) algorithm and beneficial offloading group (BOG) algorithm. BOT algorithm can obtain the threshold of each device, i.e., the maximum number of mobile devices that the device can tolerate to offload tasks simultaneously while BOG algorithm can obtain a group of beneficial offloading devices. It can be proved that OGM strategy can achieve the Nash equilibrium of MUOG problem so as to obtain the maximum number of beneficial offloading devices. Experimental comparisons verify the number of beneficial offloading users and the overhead of the mechanism among different strategies. The results show that OGM can benefit more devices by offloading to save energy without high overhead compared with other offloading strategies.