Combinatorics of Correlated Equilibria

09/28/2022

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by   Marie-Charlotte Brandenburg, et al.

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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. Through the use of the oriented matroid strata, we propose a structured method for describing the possible combinatorial types of P_G, 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.