On the Price of Anarchy of Highly Congested Nonatomic Network Games

TL;DR

This paper investigates how the inefficiency of nonatomic network games, measured by the price of anarchy, behaves as traffic inflow increases, showing it tends to one under certain conditions but not always.

Contribution

It provides an analysis of the asymptotic behavior of the price of anarchy in highly congested nonatomic network games, including conditions for convergence and counterexamples.

Findings

Price of anarchy approaches one as inflow increases under certain conditions.

Counterexamples show the price of anarchy does not always tend to one.

Simple parallel graphs can exhibit non-converging behavior.

Abstract

We consider nonatomic network games with one source and one destination. We examine the asymptotic behavior of the price of anarchy as the inflow increases. In accordance with some empirical observations, we show that, under suitable conditions, the price of anarchy is asymptotic to one. We show with some counterexamples that this is not always the case. The counterexamples occur in very simple parallel graphs.