For multi-transmission rate environments, access point (AP) connection methods have been proposed for maximizing system throughput, which is the throughput of an entire system, on the basis of the cooperative behavior of users. These methods derive optimal positions for the cooperative behavior of users, which means that new users move to improve the system throughput when connecting to an AP. Typically, the arrival of two or more new users causes signal interference for other users. Specifically, traditional methods have not considered interference and the number of allowable mobile positions is so large that it is difficult to find the optimal position to maximize system throughput. In this paper, we propose an AP connection method that maximizes system throughput by considering interference between users, with a potential game model. This game can find at least one optimal user position. Moreover, numerical analyses show the effectiveness of our method.