Subversive Conversations

Two players with common interests exchange information to make a decision. But they fear scrutiny. Their unencrypted communications will be observed by another agent with different interests who can object to their decision. We show how the players can implement their ideal 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 show how conversations can maintain deniability even in the face of leaks, hacks, and other public exposures.