Wireless stations (WSs) in an IEEE 802.11 access network compete with each other for collective bandwidth offered by access points (APs). The competition involves selecting an AP with the consideration of potential link rate and workload status. From the perspective of system, a good AP selection policy should be stable, increase overall system throughput, and maintain bandwidth fairness among WSs. This paper models AP selections under the framework of game theory, where each WS's sole goal is to maximize its achievable throughput. The achievable throughput depends on not only the number of WSs that associate with the same AP but the set of link rates these WSs use as well. It is not a monotonically decreasing function of WS population when considering the effect of performance anomaly. We have proven the stability of this game (Nash equilibrium) and shown that selfish behavior of individual WSs in fact improves overall bandwidth fairness among WSs. Thorough simulations were conducted to demonstrate the validity of the analytical results and compare the performance of the proposed game with that of counterparts.