  This paper studies a stylized model of local interaction where agents choose
from an ever increasing set of vertically ranked actions, e.g. technologies.
The driving forces of the model are infrequent upward shifts (``updates''),
followed by a rapid process of local imitation (``diffusion''). Our main focus
is on the regularities displayed by the long-run distribution of diffusion
waves and their implication on the performance of the system. By integrating
analytical techniques and numerical simulations, we come to the following two
main conclusions. (1) If dis-coordination costs are sufficiently high, the
system behaves critically, in the sense customarily used in physics. (2) The
performance of the system is optimal at the frontier of the critical region.
Heuristically, this may be interpreted as an indication that
(performance-sensitive) evolutionary forces induce the system to be placed ``at
the edge of order and chaos''
