We study the degradation in network performance caused by the 
selfish behavior of noncooperative network users.  We consider 
a directed network in which each edge possesses a latency 
function describing the common latency incurred by all traffic 
on the edge as a function of the edge congestion.  Given a rate 
of traffic between each pair of nodes in the network, we aspire 
toward an assignment of traffic to paths in which the sum of all
travel times (the {\em total latency}) is minimized; however, in 
many settings network users are free to route their traffic in a 
selfish manner, without regard to the total latency.  We 
therefore assume that each network user routes its traffic on 
the minimum-latency path available to it, given the network 
congestion caused by the other users.  In general such a 
``selfishly motivated'' assignment of traffic to paths (a {\em 
Nash equilibrium}) will not minimize the total latency; hence, 
selfish behavior carries the cost of decreased network 
performance.  We quantify this degradation in network performance 
via the {\em price of anarchy}, defined as the worst-possible 
ratio between the total latency of a Nash equilibrium and of a 
minimum-latency routing of the traffic.

In this paper, we show that the underlying network topology plays 
no role in the determination of the price of anarchy.  
Specifically, we show that under weak hypotheses on the class of 
allowable edge latency functions, the worst-case ratio between the 
total latency of a Nash equilibrium and of a minimum-latency 
routing for any multicommodity flow network is achieved by a 
single-commodity instance on a network of parallel links.  In the 
special case where the class of allowable latency functions 
includes all of the constant functions, we prove that a network 
with only two parallel links suffices to achieve the worst-possible 
ratio.  Informally, these results imply that the inefficiency 
inherent in a flow at Nash equilibrium stems from the inability of 
selfish users to discern which of two competing routes is superior 
and {\em not} from the topological complexity arising from the 
diverse intersections of many paths belonging to different 
commodities.

Our result that simple networks always furnish worst-possible 
examples also provides a powerful method for computing the price of 
anarchy with respect to an arbitrary class of latency functions.  
We apply this method to function classes that have been well 
studied in the literature (such as degree-bounded polynomials and 
functions of the form $\ell(x) = (u-x)^{-1}$ that are used to model 
edges with capacity $u$), thereby obtaining the first tight 
analyses of the price of anarchy for significant classes of latency 
functions outside the class of linear functions.