Modes of ambiguous communication

We study cheap talk communication in a simple two actions-two states model featuring an ambiguous state distribution. Equilibrium behavior of both sender (S) and receiver (R) features mixing and we relate each agent's randomization to a specific mode of ambiguous communication. For sufficiently high ambiguity, implementing the S-optimal decision rule with only two messages is impossible if R has aligned preferences. This may in contrast be possible if R has misaligned preferences. Adding a little ambiguity may generate influential communication that is unambiguously advantageous to S.