  We develop a general formalism to describe the interactions between a
discrete set of plasmonic resonators mediated by the electromagnetic field. The
resulting system of equations for closely-spaced meta-atoms represents a
cooperative metamaterial response and we find that collective interactions
between asymmetric split-ring resonators arranged in a 2D lattice explains the
recent experimental observations of system-size dependent narrowing of the
transmission resonance linewidth. We further show that this cooperative
narrowing depends sensitively on the lattice spacing.
