Coordination with Local Information

We study the role of local information channels in enabling coordination among strategic agents. Building on the standard finite-player global games framework, we show that the set of equilibria of a coordination game is highly sensitive to how information is locally shared among different agents. In particular, we show that the coordination game has multiple equilibria if there exists a collection of agents such that (i) they do not share a common signal with any agent outside of that collection; and (ii) their information sets form an increasing sequence of nested sets. Our results thus extend the results on the uniqueness and multiplicity of equilibria beyond the well-known cases in which agents have access to purely private or public signals. We then provide a characterization of the set of equilibria as a function of the penetration of the local information channels. We show that the set of equilibria shrinks as information becomes more decentralized.