Communication Complexity of Correlated Equilibrium in Two-Player Games

TL;DR

This paper establishes a linear lower bound on the communication complexity for computing approximate correlated equilibria in a specific two-player game, resolving an open problem for small approximation factors.

Contribution

It introduces the 2-cycle game and proves a tight lower bound on the communication needed, using a reduction from the unique set disjointness problem.

Findings

Linear communication complexity lower bound for the 2-cycle game

Resolution of an open question for small approximation values

Reduction from the unique set disjointness problem

Abstract

We show a communication complexity lower bound for finding a correlated equilibrium of a two-player game. More precisely, we define a two-player $N \times N$ game called the 2-cycle game and show that the randomized communication complexity of finding a 1/poly($N$)-approximate correlated equilibrium of the 2-cycle game is $\Omega(N)$. For small approximation values, this answers an open question of Babichenko and Rubinstein (STOC 2017). Our lower bound is obtained via a direct reduction from the unique set disjointness problem.