The epistemic spirit of divinity

We study strategic reasoning in a signaling game where players initially have common belief in an outcome distribution and in the event that the sender's beliefs are independent of her type. We characterize the behavioral implications of these epistemic hypotheses by means of a rationalizability procedure with belief restrictions. Our solution concept is related to, but weaker than Divine Equilibrium (Banks & Sobel, Econometrica 1987). First, we do not obtain a sequential equilibrium, but just a perfect Bayesian equilibrium with heterogeneous off-path beliefs (Fudenberg & He, Econometrica 2018). Second, when we model how the receiver may rationalize a particular deviation, we take into account that some types could have preferred a different deviation, and we show this is natural and relevant via an economic example.