Equilibrium selection in power control games on the interference channel

In recent years, game-theoretic tools have been increasingly used to study many important resource allocation problems in communications and networking. One common feature shared by all these approaches is that, when it comes to (distributed) computation of equilibria, assumptions are always made that imply uniqueness of the Nash Equilibrium. This simplifies considerably the analysis of the games under investigation and permits to design distributed solution methods with convergence guarantee. However, requiring the uniqueness of the solution may be too demanding in many practical situations, thus strongly limiting the applicability of current game theoretical methodologies. In this paper, we overcome this limitation and propose novel distributed algorithms for noncooperative games having multiple solutions. The new methods, whose convergence analysis is based on variational inequality techniques, are able to select, among all the equilibria of a game, those which optimize a given performance criterion. We apply the developed methods to a power control problem over parallel Gaussian interference channels and show that they yield a considerable performance improvement over classical power control schemes.