We analyze how dynamic information should be provided to uniquely implement the largest equilibrium in binary-action coordination games. The designer offers an informational put: she stays silent if players choose her preferred action, but injects asymmetric and inconclusive public information if they lose faith. There is (i) no multiplicity gap: the largest (partially) implementable equilibrium can be implemented uniquely; and (ii) no commitment gap: the policy is sequentially optimal. Our results have sharp implications for the design of policy in coordination environments.

We analyze inertial coordination games: dynamic coordination games with an endogenously changing state that depends on (i) a persistent fundamental that players privately learn about; and (ii) past play. We give a tight characterization of how the speed of learning shapes equilibrium dynamics: the risk-dominant action is selected in the limit if and only if learning is slow such that posterior precisions grow sub-quadratically. This generalizes results from static global games and endows them with an alternate learning foundation. Conversely, when learning is fast, equilibrium dynamics exhibit persistence and limit play is shaped by initial play. Whenever the risk dominant equilibrium is selected, the path of play undergoes a sudden transition when signals are precise, and a gradual transition when signals are noisy.