The geometry of Nash equilibria and correlated equilibria and a generalization of zero-sum games - Yannick Viossat (Stockholm School of Economics, The Economic Research Institute (EFI), 2006)
A pure strategy is coherent if it is played with positive probability in at least one correlated equilibrium. A game is pre-tight if in every correlated equilibrium, all incentives constraints for non deviating to a coherent strategy are tight. We show that there exists a Nash equilibrium in the relative interior of the correlated equilibrium polytope if and only if the game is pre-tight. Furthermore, the class of pre-tight games is shown to include and generalize the class of two-player zero-sum games.
Keywords: C72; 330; correlated equilibrium; Nash equilibrium; zero-sum games; dual reduction; Spieltheorie; Nash-Gleichgewicht