Selfishness need not be bad: a general proof

TL;DR

This paper develops a unified framework to analyze the asymptotic behavior of the price of anarchy in non-atomic congestion games, showing that selfish behavior can be benign under broad conditions.

Contribution

It introduces new techniques for limit analysis of the price of anarchy, generalizing previous results to arbitrary polynomial and regularly varying price functions.

Findings

Global convergence of the price of anarchy for polynomial price functions

Applicability to non-polynomial, regularly varying price functions

Selfishness can be non-detrimental in broad classes of congestion games

Abstract

This article studies the user behavior in non-atomic congestion games. We consider non-atomic congestion games with continuous and non-decreasing functions and investigate the limit of the price of anarchy when the total user volume approaches infinity. We deepen the knowledge on {\em asymptotically well designed games} \cite{Wu2017Selfishness}, {\em limit games} \cite{Wu2017Selfishness}, {\em scalability} \cite{Wu2017Selfishness} and {\em gaugeability} \cite{Colini2017b} that were recently used in the limit analyses of the price of anarchy for non-atomic congestion games. We develop a unified framework and derive new techniques that allow a general limit analysis of the price of anarchy. With these new techniques, we are able to prove a global convergence on the price of anarchy for non-atomic congestion games with arbitrary polynomial price functions and arbitrary user volume vector sequences. Moreover, we show that these new techniques are very flexible and robust and apply also to non-atomic congestion games with price functions of other types. In particular, we prove that non-atomic congestion games with regularly varying price functions are also asymptotically well designed, provided that the price functions are slightly restricted. Our results greatly generalize recent results. In particular, our results further support the view with a general proof that selfishness need not be bad for non-atomic congestion games.