Endogenous ambiguity and rational miscommunication

This paper studies a sender-receiver game in which both players want the receiver to choose the state-optimal action. Before observing the state, the sender observes a “contextual signal,” a payoff-irrelevant signal that correlates with states and is imperfectly shared with the receiver. Once the sender observes the state, the sender sends a message to the receiver, incurring a small messaging cost. It is shown that there is no miscommunication in any efficient equilibrium if the messaging cost is uniform or contextual information is poorly shared between players. However, if the messaging costs are different between some messages, and contextual information can affect the probability ranking of states and is shared reasonably well, any efficient equilibrium that favors the sender exhibits miscommunication. Furthermore, the messages that cause miscommunication can be coarse or ambiguous, depending on how well players share contextual information.