Parameterized Two-Player Nash Equilibrium

TL;DR

This paper investigates the parameterized complexity of computing Nash equilibria in two-player games, identifying cases where the problem is fixed-parameter tractable, including sparse, unbalanced, and locally bounded treewidth games.

Contribution

It extends previous hardness results by showing fixed-parameter tractability in new game classes, notably locally bounded treewidth games.

Findings

Fixed-parameter tractability in sparse and unbalanced games

Introduction of locally bounded treewidth games as a tractable case

Generalization of previous results to broader game classes

Abstract

We study the computation of Nash equilibria in a two-player normal form game from the perspective of parameterized complexity. Recent results proved hardness for a number of variants, when parameterized by the support size. We complement those results, by identifying three cases in which the problem becomes fixed-parameter tractable. These cases occur in the previously studied settings of sparse games and unbalanced games as well as in the newly considered case of locally bounded treewidth games that generalizes both these two cases.