Mode 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 typically mixes between messages triggering different behavior by R while R himself mixes after some message. Technically, the mixing performed by S is equivalent to mixing over classical partitional strategies. We interpret mixing by respectively S or 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, though only two actions are available to R. If only two messages are available and S faces his preference twin, he may be unable to implement his optimal decision rule and influential communication may be altogether impossible. We remark that these results would not emerge in an expected utility environment. Third, we find that there often exist influential equilibria that do not implement the optimal decision rule of S, which is not the case in the absence of ambiguity. Fourth, we show that the addition of a little ambiguity may generate influential communication that is unambiguously advantageous to S. Fifth, we consider a smooth version of our model and find that some of our key findings extend to this setting.