The set of correlated equilibria is convex and contains all Nash equilibria as special cases. Thus, the social welfare-maximizing correlated equilibrium is amenable to convex analysis and offers social welfare that is at least as good as the game’s best performing Nash equilibria.We employ robust semidefinite programming (SDP) for computing the social welfare-maximizing correlated equilibria in static polynomial games, giving rise to a dedicated sequential SDP algorithm, the first of this type that can cope with multivariate strategy sets. We apply this algorithm to a wireless communication problem, where two mutually-interfering transmitters and receivers maximize their channel capacities.