On the performance of approximate equilibria in congestion games

TL;DR

This paper analyzes how the efficiency of approximate Nash equilibria in linear congestion games varies with the approximation factor, providing tight bounds and unifying atomic and non-atomic cases.

Contribution

It offers (almost) tight bounds for the price of anarchy and stability in approximate equilibria, extending and unifying existing results for exact equilibria.

Findings

Bounds for price of anarchy and stability as functions of epsilon

Unified approach for atomic and non-atomic congestion games

Pigou network results extend to epsilon-Nash equilibria

Abstract

We study the performance of approximate Nash equilibria for linear congestion games. We consider how much the price of anarchy worsens and how much the price of stability improves as a function of the approximation factor $\epsilon$. We give (almost) tight upper and lower bounds for both the price of anarchy and the price of stability for atomic and non-atomic congestion games. Our results not only encompass and generalize the existing results of exact equilibria to $\epsilon$-Nash equilibria, but they also provide a unified approach which reveals the common threads of the atomic and non-atomic price of anarchy results. By expanding the spectrum, we also cast the existing results in a new light. For example, the Pigou network, which gives tight results for exact Nash equilibria of selfish routing, remains tight for the price of stability of $\epsilon$-Nash equilibria but not for the price of anarchy.