The Complexity of Approximating a Trembling Hand Perfect Equilibrium of a Multi-player Game in Strategic Form

Kousha Etessami, Kristoffer Arnsfelt Hansen, Peter Bro Miltersen, Troels Bjerre Sørensen

Abstract: We consider the task of computing an approximation of a trembling hand perfect equilibrium for an n-player game in strategic form, n ≥ 3. We show that this task is complete for the complexity class FIXP a . In particular, the task is polynomial time equivalent to the task of computing an approximation of a Nash equilibrium in strategic form games with three (or more) players.