A Direct Reduction from k-Player to 2-Player Approximate Nash Equilibrium

TL;DR

This paper introduces a direct reduction method from k-player to 2-player games for approximate Nash equilibrium, simplifying previous complex reductions and avoiding the PPAD complexity class framework.

Contribution

It provides the first direct reduction from k-player to 2-player approximate Nash equilibrium, removing reliance on PPAD-based indirect reductions.

Findings

Simplifies the reduction process between k-player and 2-player games

Eliminates the need for PPAD complexity class framework

Facilitates easier analysis of approximate Nash equilibria

Abstract

We present a direct reduction from k-player games to 2-player games that preserves approximate Nash equilibrium. Previously, the computational equivalence of computing approximate Nash equilibrium in k-player and 2-player games was established via an indirect reduction. This included a sequence of works defining the complexity class PPAD, identifying complete problems for this class, showing that computing approximate Nash equilibrium for k-player games is in PPAD, and reducing a PPAD-complete problem to computing approximate Nash equilibrium for 2-player games. Our direct reduction makes no use of the concept of PPAD, thus eliminating some of the difficulties involved in following the known indirect reduction.