Subversive Conversations

Two players with common interests exchange information to make a decision. Their communication is scrutinized by an observer with different interests who understands the meaning of all messages and may object to the decision. We show how the players can implement their optimal decision rule using a back and forth conversation. Such a subversive conversation reveals enough information for the players to determine their best decision, but not enough information for the observer to determine whether the decision was against his interest. Our results provide a theory of conversations based on deniability in the face of possible public outrage.