Coordination with Rational Inattention

We study information acquisition in a coordination game with incomplete information. To capture the idea that players can flexibly decide what information to acquire, we do not impose any physical restriction on the set of feasible information structures. Facing an informational cost measured by reduction of Shannon's entropy, players collect information most relevant to their welfare and are rationally inattentive to other aspects. When coordination is valuable and information is cheap, endogenous and flexible information acquisition enables players to acquire information that makes efficient coordination possible, but also gives rise to multiple equilibria. This contrasts with the global game literature, where information structure is less flexible and cheap information leads to unique equilibrium with inefficient coordination. This distinction results from the difference between the flexible information structure of our approach and the rigidity implicitly imposed on the information structure of global game models. We also provide a clear and intuitive condition for the emergence of multiplicity in terms of the relative magnitude of strategic complementarity and informational cost.