  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. Our proposed algorithm is a modified
Fictitious Play algorithm that can be implemented distributedly and its stable
points are the pure Nash equilibria of a given game. Our goal is to design a
utility function for a non-cooperative game such that all of its pure Nash
equilibria have close to optimal global performance. This will make the
algorithm close to optimal while requiring no communication between users. We
propose a novel technique to analyze the Nash equilibria of a random
interference game, determined by the random channel gains. Our analysis is
asymptotic in the number of users. First we present a natural non-cooperative
game where the utility of each user is his achievable rate. It is shown that,
asymptotically in the number of users and for strong enough interference, this
game exhibits many bad equilibria. Then we propose a novel non-cooperative M
Frequency-Selective Interference Channel Game (M-FSIG), as a slight
modification of the former, where the utility of each user is artificially
limited. We prove that even its worst equilibrium has asymptotically optimal
weighted sum-rate for any interference regime and even for correlated channels.
This is based on an order statistics analysis of the fading channels that is
valid for a broad class of fading distributions (including Rayleigh, Rician,
m-Nakagami and more). We carry out simulations that show fast convergence of
our algorithm to the proven asymptotically optimal pure Nash equilibria.
