Near-Optimal Communication Lower Bounds for Approximate Nash Equilibria

TL;DR

This paper establishes a near-quadratic lower bound on the amount of communication needed between two players to find an approximate Nash equilibrium in a large game, highlighting fundamental complexity limits.

Contribution

It provides the first near-optimal lower bound for the communication complexity of computing approximate Nash equilibria in two-player games.

Findings

Proves an $N^{2-o(1)}$ lower bound on communication complexity.

Shows the inherent difficulty of computing approximate Nash equilibria.

Highlights fundamental limits in game-theoretic computation.

Abstract

We prove an $N^{2-o(1)}$ lower bound on the randomized communication complexity of finding an $\epsilon$-approximate Nash equilibrium (for constant $\epsilon>0$) in a two-player $N\times N$ game.