On the Hardness and Existence of Quasi-Strict Equilibria

This paper investigates the computational properties of quasi-strict equilibrium, an attractive equilibrium refinement proposed by Harsanyi, which was recently shown to always exist in bimatrix games. We prove that deciding the existence of a quasi-strict equilibrium in games with more than two players is NP-complete. We further show that, in contrast to Nash equilibrium, the support of quasi-strict equilibrium in zero-sum games is unique and propose a linear program to compute quasi-strict equilibria in these games. Finally, we prove that every symmetric multi-player game where each player has two actions at his disposal contains an efficiently computable quasi-strict equilibrium which may itself be asymmetric.