Abstract
We study the correlated equilibrium polytope PG 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 PG , and show that for ( 2 × 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 × 3 ) -games.
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