The complexity of approximating a trembling hand perfect equilibrium of a multi-player game in strategic form

TL;DR

This paper proves that approximating a trembling hand perfect equilibrium in multi-player strategic form games is computationally as hard as finding approximate Nash equilibria, establishing its FIXP_a-completeness.

Contribution

It demonstrates the FIXP_a-completeness of approximating trembling hand perfect equilibria for multi-player games, linking it to the complexity of computing approximate Nash equilibria.

Findings

The task is FIXP_a-complete.

Computing an approximation is polynomial time equivalent to Nash equilibrium approximation.

The result applies to games with three or more players.

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.