This note offers characterizations of tightness and weak tightness. It shows that when the preference domain is that of continuous utility functions on the outcome space, the two notions are equivalent to the outcome closure property of Milgrom (2010a).

This paper makes a first attempt at building a theory of interim Bayesian persuasion. I work in a minimalist model where a low or high type sender seeks validation from a receiver who is willing to validate high types exclusively. After learning her type, the sender chooses a complete...