Bandwidth allocation games under budget and access constraints

We study bandwidth allocation at base stations of a wireless network as a non-cooperative game between different wireless users. A user demands bandwidth from the base stations it has access to by submitting bids. Once the bidding process is complete, a base station distributes its bandwidth to the users in proportion to their bids. Users are assumed to be budget constrained and price anticipating, and split their wealth across base stations so as to maximize their individual bandwidths. In this paper, we study the properties of Nash Equilibrium (NE) for this bandwidth allocation game. For the special case where each user can access all base stations, we argue that there exists a unique NE, at which the bandwidth obtained by any user is proportional to its wealth. For a more general scenario where a user may be able to access only a subset of all base stations, we compare the NE of the game to the max-min fair bandwidth allocation. We show that although the NE may not be max-min fair in general, the bandwidth allocation at NE becomes arbitrarily close to max-min fair allocation as the number of users is increased, while keeping the number of base stations fixed.