Communication complexity of approximate Nash equilibria

TL;DR

This paper establishes significant lower bounds on the communication complexity required to compute approximate Nash equilibria in multi-player games, revealing fundamental limits in distributed game-theoretic computations.

Contribution

It provides the first polynomial lower bound for two-player approximate Nash equilibria and an exponential lower bound for multi-player weak approximate equilibria.

Findings

Poly(N) lower bound for two-player epsilon-Nash equilibria.

Exponential lower bound for n-player weak approximate Nash equilibria.

Highlights the communication complexity challenges in distributed game solutions.

Abstract

For a constant $\epsilon$, we prove a poly(N) lower bound on the (randomized) communication complexity of $\epsilon$-Nash equilibrium in two-player NxN games. For n-player binary-action games we prove an exp(n) lower bound for the (randomized) communication complexity of $(\epsilon,\epsilon)$-weak approximate Nash equilibrium, which is a profile of mixed actions such that at least $(1-\epsilon)$-fraction of the players are $\epsilon$-best replying.