Modes of ambiguous communication

We study cheap talk communication in a simple two actions-two states model featuring ambiguous priors. First, we find that in equilibrium, S often mixes between messages triggering different beliefs and behavior by R while R also occasionally randomizes. We interpret randomization by respectively S and R as embodying two different modes of ambiguous communication. Second, we find that for sufficiently high ambiguity, more than two messages are often necessary to implement the optimal decision rule of S. If only two messages are available and S faces his preference twin, S may be unable to implement his optimal decision rule and influential communication may be altogether impossible. We stress the non replicability of these results within an expected utility environment. Third, we show that the addition of a little ambiguity
may generate influential communication that is unambiguously advantageous to
S.