In this talk we discuss the correlated equilibrium polytope P of a game G from a combinatorial point of view.  We introduce the region of full-dimensionality for this class of polytopes, and prove that it is a semialgebraic set for any game. Through the use of the oriented matroid strata, we propose a structured method for describing the possible combinatorial types of P, and show that for (2×n)-games, the algebraic boundary of each stratum is the union of coordinate hyperplanes and binomial hypersurfaces. Finally, we provide a computational proof that there exists a unique combinatorial type of maximal dimension for (2×3)-games. This is joint work with Marie-Charlotte Brandenburg and Irem Portakal.