Belief inducibility and informativeness

We consider a group of receivers who share a common prior on a finite state space and who observe private correlated messages that are contingent on the true state of the world. Our focus lies on the beliefs of receivers induced via the signal chosen by the sender and we provide a comprehensive analysis of the inducible distributions of posterior beliefs. Classifying signals as minimal, individually minimal, and language-independent, we show that any inducible distribution can be induced by a language-independent signal. We investigate the role of the different classes of signals for the amount of higher order information that is revealed to receivers. The least informative signals that induce a fixed distribution over posterior belief profiles lie in the relative interior of the set of all language-independent signals inducing that distribution.