Observing Actions in Bayesian Games

We study Bayesian coordination games where agents receive noisy private information over the game's payoff structure, and over each others' actions. If private information over actions is precise, we find that agents can coordinate on multiple equilibria. If private information over actions is of low quality, equilibrium uniqueness obtains like in a standard global games setting. The current model, with its flexible information structure, can thus be used to study phenomena such as bank-runs, currency crises, recessions, riots, and revolutions, where agents rely on information over each others' actions.