Full revelation of information in Sender–Receiver games of persuasion

We provide necessary and sufficient conditions on both players' preferences and information that can be certified for a Sender–Receiver game to possess a separating equilibrium, as well as sufficient conditions for every equilibrium of such a game to be separating. Accordingly, we generalize Seidmann and Winter's [D.J. Seidmann, E. Winter, Strategic information transmission with verifiable messages, Econometrica 65 (1997) 163–170] results to games with partial provability.