  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.
