Equilibrium selection in MIMO communication games

In recent years, game-theoretic tools have been increasingly used to study many important resource allocation problems in communications and networking. When it comes to (distributed) computation of equilibria, two common issues arise from current approaches, namely: i) the best-response mapping of each player must be unique and is required to be computed in closed form; and ii) convergence of proposed algorithms is obtained only under conditions implying the uniqueness of the Nash Equilibrium. Even thought these assumptions simplify considerably the analysis of the games under investigation, they may be too demanding in many practical situations, thus strongly limiting the applicability of current methodologies to games with arbitrary objective functions and strategy sets. In this paper, we overcome these limitations and propose novel distributed algorithms for arbitrary noncooperative games having (possibly) 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, at the cost of limited signaling among the players. We then apply the developed methods to solve a MIMO game in cognitive radios, showing a considerable performance improvement over classical pure noncooperative schemes.