A user located in a congested area of a wireless LAN may benefit by moving to a less-crowded area and using a less-loaded access point. This idea has gained attention from researchers in recent literature , . However, its effectiveness and stability are questionable. Each user selects the access point that offers the optimal trade-off between load and distance to be traveled. Since users are selfish, a user's selection may adversely impact other users, in turn motivating them to change their selections. Also, future user arrivals and exits may invalidate current selections. This paper presents the first game-theoretic analysis of this idea. We model access point selection as a game, characterize the Nash equilibria of the system and examine distributed myopic selections that naturally mimic selfish users. We analytically and empirically assess the impact of user diversity and dynamic exit patterns on system behavior. The paper contributes to a deeper understanding of the costs, benefits and stability of such a solution in various usage scenarios, which is an essential pre-requisite for real-world deployment.