  When many independent users try to route traffic through a network, the flow
can easily become suboptimal as a consequence of congestion of the most
efficient paths. The degree of this suboptimality is quantified by the
so-called "price of anarchy" (POA), but so far there are no general rules for
when to expect a large POA in a random network. Here I address this question by
introducing a simple model of flow through a network with randomly-placed
"congestible" and "incongestible" links. I show that the POA is maximized
precisely when the fraction of congestible links matches the percolation
threshold of the lattice. Both the POA and the total cost demonstrate critical
scaling near the percolation threshold.
