Cheap Talk with Coarse Understanding

We use the analogy-based expectation equilibrium (Jehiel, 2005) to study cheap talk from a sender who does not perfectly understand all the messages available to him. The sender is endowed with a privately known language competence corresponding to the set of messages that he understands. For the messages that he does not understand, the sender has correct but only coarse expectations about the equilibrium response of the receiver. An analogy-based expectation equilibrium is always a Bayesian solution but usually differs from a standard communication equilibrium and from an equilibrium with language barriers (Blume and Board, 2013). We characterize conditions under which an outcome remains an equilibrium outcome when the sender's competence decreases. Partial language competence rationalizes information transmission and lies in pure persuasion problems, and can facilitate information transmission from a moderately biased sender.