Underreaction and dynamic inconsistency in communication games under noise

Abstract: Communication is rarely perfect, but rather prone to error of transmission and reception. Often the origin of these errors cannot be properly quantified and is thus imprecisely known. We analyze the impact of an ambiguous noise which may alter the received message on a communication game of common interest. The noise is ambiguous in the sense that the parameters of the error-generating process and thus the likelihood to receive a message by mistake are Knightianly unknown. Ex-ante and interim responses are characterized under maxmin preferences. While the sender can disregard ambiguity, the receiver reveals a dynamically inconsistent, but astonishing behavior under a quadratic loss. Their interim actions will be closer to the pooling action than their ex-ante ones, as if facing a higher likelihood of an occurring error.