Signaling covertly acquired information

We study the interplay between information acquisition and signaling. A sender decides whether to learn his type at a cost prior to taking a signaling action. A receiver observes the signaling action and responds. We characterize equilibria and apply a version of never a weak best response refinement in the environment where the information acquisition is observable as well as in the environment where it is covert. Covert information acquisition always leads to information acquisition when information is cheap. Observable information acquisition, on the other hand, does not necessarily.