Correlated equilibria are a generalization of Nash equilibria. Existence of a correlated equilibrium is guaranteed due to existence of a Nash equilibrium. In this talk I will present a result of Germano & Lugosi(2007) that shows every finite normal form game possesses a sparsely supported correlated equilibrium.
Ref: Fabrizio Germano & Gábor Lugosi, 2007. "Existence of Sparsely Supported Correlated Equilibria," Economic Theory, Springer, vol. 32(3), pages 575-578, September.