Coordination on Networks

We study a coordination game among agents on a network, choosing whether or not to take an action that yields value increasing in the actions of neighbors. In a standard global game setting, players receive noisy information of the technology’s common state-dependent value. We show the existence and uniqueness of a pure equilibrium in the noiseless limit. This equilibrium partitions players into coordina- tion sets, within members take a common cutoff strategy and are path connected. We derive an algorithm for calculating limiting cutoffs, and provide necessary and sufficient conditions for agents to inhabit the same coordination set. The strategic effects of perturbations to players’ underlining values are shown to spread throughout but be contained within the perturbed players’ coordination sets.