Communication complexity of Nash equilibrium in potential games

TL;DR

This paper establishes fundamental lower bounds on the communication complexity required to compute Nash equilibria in potential games, demonstrating inherent computational hardness in these strategic settings.

Contribution

It provides the first known communication complexity lower bounds for computing Nash equilibria in potential games, highlighting their computational difficulty.

Findings

Poly(N) communication lower bound for two-player N x N potential games

Exponential (2^{poly(n)}) communication lower bound for n-player two-action games

First demonstration of hardness results for Nash equilibrium in potential games

Abstract

We prove communication complexity lower bounds for (possibly mixed) Nash equilibrium in potential games. In particular, we show that finding a Nash equilibrium requires $poly(N)$ communication in two-player $N \times N$ potential games, and $2^{poly(n)}$ communication in $n$-player two-action games. To the best of our knowledge, these are the first results to demonstrate hardness in any model of (possibly mixed) Nash equilibrium in potential games.