Computational Complexity of Computing a Quasi-Proper Equilibrium

Kristoffer Arnsfelt Hansen, Troels Bjerre Lund

Abstract: We study the computational complexity of computing or approximating a quasi-proper equilibrium for a given finite extensive form game of perfect recall. We show that the task of computing a symbolic quasi-proper equilibrium is \(\mathrm {PPAD}\)-complete for two-player games. For the case of zero-sum games we obtain a polynomial time algorithm based on Linear Programming. For general n-player games we show that computing an approximation of a quasi-proper equilibrium is \(\mathrm {FIXP}_a\)-complete. Towards our results for two-player games we devise a new perturbation of the strategy space of an extensive form game which in particular gives a new proof of existence of quasi-proper equilibria for general n-player games.