  In this paper we consider the problem of distributed channel allocation in
large networks under the frequency-selective interference channel. Performance
is measured by the weighted sum of achievable rates. First we present a natural
non-cooperative game theoretic formulation for this problem. It is shown that,
when interference is sufficiently strong, this game has a pure price of anarchy
approaching infinity with high probability, and there is an asymptotically
increasing number of equilibria with the worst performance. Then we propose a
novel non-cooperative M Frequency-Selective Interference Game (M-FSIG), where
users limit their utility such that it is greater than zero only for their M
best channels, and equal for them. We show that the M-FSIG exhibits, with high
probability, an increasing number of optimal pure Nash equilibria and no bad
equilibria. Consequently, the pure price of anarchy converges to one in
probability in any interference regime. In order to exploit these results
algorithmically we propose a modified Fictitious Play algorithm that can be
implemented distributedly. We carry out simulations that show its fast
convergence to the proven pure Nash equilibria.
