We study global games in which agents coordinate with network neighbors, contingent on a favorable state. Each agent observes private signals within an expanding radius. Although agents eventually learn the state, efficient coordination also requires higher-order beliefs, which depend on network geometry. We define network common learning to capture when learning leads to efficient coordination. It holds when neighbors observe many different signals, as on the two-dimensional grid, but fails on networks with bottlenecks, such as the line.

We study a pure coordination game on a large social network. Coordination is local. We ask when equilibria can be highly efficient, meaning that most neighbors choose the same action. We show that this is possible if and only if the network is amenable, and construct leader equilibria that achieve it.

Many schools across the world rely on centralized admissions systems. A key problem is that some mechanisms give students incentives to manipulate reports, which can distort outcomes and harm others. We compare mechanisms using robustness to manipulations, measuring how much a student can expand the set of schools they can reach via a misreport. This strengthens existing manipulability comparisons and helps rationalize recent reforms.