Local Coordination and the Geometry of Social Networks

We study agents playing a pure coordination game on a large network. Agents
are restricted to coordinate locally, without access to a global communication device,
and so different regions of the network will converge to different actions, precluding
perfect coordination. We show that the extent of this inefficiency depends on the
network geometry: on some networks, near-perfect efficiency is achievable, while on
others welfare is strictly bounded away from the optimum. We provide a geometric
condition on the network structure that characterizes when near-efficiency is attainable.
On networks in which it is unattainable, our results more generally preclude high
correlations between outcomes in a large spectrum of dynamic games.