Base Station Association Game in Multi-cell Wireless Networks

We consider a multi-cell wireless network with a large number of users. Each user selfishly chooses the Base Station (BS) that gives it the best throughput (utility), and each BS allocates its resource by some simple scheduling policy. First we consider two cases: (1) BS allocates the same time to its users; (2) BS allocates the same throughput to its users. It turns out that, combined with users' selfish behavior, case (1) results in a single Nash Equilibrium (NE), which achieves system-wide Proportional Fairness. On the other hand, case (2) results in many possible Nash Equilibria, some of which are very inefficient. Next, we extend (1) to the case where the users have general concave untility functions. It is shown tha the if each BS performs intra- cell optimization, the total utility of all users is maximized at NE. This suggests that under our model, the task of joining the "correct" BS can be left to individual users, leading to a distributed solution.