We study the correlated equilibrium polytope $P_G$ 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. Using a stratification via oriented matroids, we propose a structured method for describing the possible combinatorial types of $P_G$, and show that for $(2 \times n)$-games, the algebraic boundary of the stratification is a union of coordinate hyperplanes and binomial hypersurfaces. Finally, we provide a computational proof that there exists a unique combinatorial type of maximal dimension for generic $(2 \times 3)$-games.

翻译：我们从组合学角度研究博弈$G$的相关均衡多面体$P_G$。引入此类多面体全维性区域，并证明该区域对任意博弈均为半代数集。通过定向拟阵分层方法，提出描述$P_G$可能组合类型的结构化方案，并证明对$(2 \times n)$博弈，分层的代数边界由坐标超平面与二项式超曲面之并构成。最后，通过计算证明对于一般$(2 \times 3)$博弈，存在唯一最大维数的组合类型。